The Hatters won 2-0 on Tuesday, overcoming a 2-1 first-leg deficit to progress 3-2 on aggregate amid joyous scenes at Kenilworth Road.
Defenders Gabe Osho and Tom Lockyer got the first-half goals which turned the tie around and left Edwards full of pride.
He said: “I thought over the two games we deserved it.
“They (Sunderland) had their moments and they’ve got some really good players.
“We could have been better (on Saturday), they won the game but we limited them to few chances there. But tonight we were exceptional.
“We’ve got to stick to what we’re good at and we did that tonight. I’m so pleased for the supporters and everyone at the club.
“To do it here (Kenilworth Road) is really special. We knew where our advantages lay, we scored a couple of good goals but I think we could have had a lot more as well. It was a really strong performance.”
The Hatters can look forward to a Wembley showdown against Coventry or Middlesbrough on May 27, with a place in the Premier League the prize to the winner.
Luton have not played top-flight football since 1992 and Edwards continued: “It wasn’t about us doing a job on Sunderland, it was about us being really good.
“We limited them to shots from distance, one save Ethan (Horvath) made over the 94 minutes.”
Sunderland boss Tony Mowbray was frustrated a season of such promise ended in defeat.
The Black Cats were promoted to the Championship via the play-offs last May and Mowbray said: “I’m frustrated but very proud of the players, the team and the city of Sunderland. We’ll get stronger and we’ll be back next season.
“I’ve only been here nine months and these players have given everything they’ve got.
“I’m proud of these young lads who week in, week out have given what they’ve got.
“We came out of League One and maybe consolidation is what people were thinking about.
“We’ve managed to punch above mediocrity. We’ve come close but unfortunately we’ve fallen short tonight.
“I think the league will be stronger next season. We have to keep building and growing and get better.”
Mowbray acknowledged that his quest for a second successive promotion was not helped by injuries.
“We’ve had huge losses of some very, very important footballers,” he said. (Captain) Corry Evans, the centre-forward who scores all the goals (Ross Stewart) and three centre-halves.
“They’ve performed really well and I’m proud of them.”
Forest led 2-0 in the 83rd minute through Chris Wood’s second-half double, but Chiedozie Ogbene gave the Hatters a late lifeline and Adebayo’s superb effort snatched them a point.
The 25-year-old took Tom Lockyer’s long ball into the box on his chest and buried a low shot in the second minute of added time as Luton, promoted via the play-offs in May, registered just their fifth point from nine matches.
Edwards said: “It was a great goal. He’s got those moments. He came on against Burnley and got his goal and he’s done it again today.
“He’s got these little moments of magic in him. The assist he got at Sheffield United, the assist at Wembley. He’s had big moments for us Eli since we’ve been here.
“He was frustrated not to start the game as I would expect, but that’s what you’ve got to do when you come on. That’s what I want. He gives me a difficult decision to make next week.”
Forest were worthy of their 2-0 lead after Wood struck in the 48th and 76th minute, but Luton refused to surrender.
Ogbene lashed home in the 83rd minute after Forest had failed to clear a free-kick and Adebayo, a second-half replacement for Pelly Ruddock Mpanzu, had the final word.
Edwards added: “I’m really proud of the players. The spirit, the fight and determination.
“We finish the game strongly. We will never give up, we will always keep fighting.
“We’re where we expected to be. Nobody expects us to be top four. We’re where we expected to be, in the fight we expected to be in. We’re comfortable with it.”
Nottingham Forest boss Steve Cooper could not hide his frustration after his side’s winless run was extended to five matches.
“It’s disappointment in the end,” Cooper said. “We dominated the game and we’re disappointed we weren’t leading by one or two goals at half-time.
“We obviously got the early goal in the second half and then made it 2-0 and it all changes on a set-piece, which we defended terribly really.
“Of all Luton’s threats off set-plays, it was the worst delivery of the day and ends up in the back of our net and that’s where the momentum changes.
“It’s a real pity because of the way we had played for however long it was before their first goal went in because it was a comfortable game for us.”
It was Luton’s first game since Lockyer suffered a cardiac arrest during last Saturday’s abandoned game away to Bournemouth.
The 29-year-old’s name was sung around Kenilworth Road throughout the contest, with the club having laid out his strip pre-match in their dressing room in tribute.
Andros Townsend headed the only goal in the first half, stealing in at the back post after Ross Barkley had flicked on a corner from Alfie Doughty and nodding beyond Martin Dubravka to a deafening roar from the home fans.
Newcastle piled on pressure in pursuit of a way back but it was Edwards’ side who came closest to adding to their tally.
First Barkley slammed an effort off the underside of the bar, a rasping 30-yard drive that beat Dubravka at full stretch, before Jacob Brown did the same in the second half after being played through by good work from Elijah Adebayo.
Alexander Isak thought he had equalised, sliding the ball into the far corner past Thomas Kaminski from Miguel Almiron’s pass, only for VAR to judge he had strayed fractionally offside.
Edwards said his team had gone into the game looking to win it for their absent captain, who was discharged from hospital on Thursday.
“I’m immensely proud of everyone,” he said. “This has been a really challenging week. They don’t teach you this on the coaching courses. I’ve needed my team around me.
“The players have been amazing, really brave. We’ve rallied around each other.
“It’s been hard to concentrate on a game of football this week. My focus has been on Tom and has family, but then there’s been a job to do, an important Premier League game. We’ve all helped each other.
“The performance was probably the most complete performances we’ve had this season.
“We’ve been playing really well. I don’t think it’s because of what’s happened that we’ve won the game today.
“We talked about it, we wanted to do it for Tom. But I don’t think there was any extra motivation there. Today we embodied everything that Tom Lockyer is.”
The result puts Luton to within a win of Nottingham Forest who were beaten 3-2 by a last-gasp goal at home to Bournemouth.
Despite an important three points, Edwards’ focus after the game was firmly on Lockyer.
“Today was about doing it for Tom,” he said. “He’s a leader and an inspiration figure for us.
“A football match pales in insignificance in that moment. It still feels a bit weird me coming in here, talking about a game of football.
“When you’re talking about someone’s life, it doesn’t matter then.”
Newcastle boss Eddie Howe reflected on a disappointing loss which was his team’s fourth in a row away from St James’ Park.
“We’ve spoken about it internally, we know how important away form is,” he said.
“We have to be consistent in home and away form. It epitomised our away form today, we didn’t compete well in the first half. We were reactive instead of proactive.
“We have an incredible group but I was disappointed with the first half, I thought we needed more emotions and energy in our performance.”
The Hatters’ dreams of reaching the Premier League for the first time in their history suffered a setback on Saturday after Sunderland hit back from an early deficit to claim a 2-1 win at the Stadium of Light.
And Luton boss Edwards has stressed the need for his side to combine a red-hot desire with ice-cold thinking if they are to book a place in the play-off final against either Middlesbrough or Coventry at Wembley later this month.
“We have got to be calm because we need 11 players on the pitch, but we need fire and then to be ice cold in the right moments,” he said.
“We need to play with real fire and like our lives depend on it tomorrow. We don’t want this to be the end but this could be our last game of the season and we don’t want that to be the case.”
Edwards echoed that message to the Luton supporters who he believes will play a vital role in deciding the outcome of Tuesday’s clash at a sold-out Kenilworth Road.
He referenced last month’s derby victory over Watford and called for a similarly “amazing” atmosphere in order to galvanise his side’s attempted fightback.
“We want the crowd to be wild and right at it,” Edwards said.
“We’ve got to make it really difficult for them and we need our crowd to play their part in that as well. And we want to make sure we play our part and give our fans something to shout about.
“The atmosphere was amazing for the Watford game and if we can notch it up a little bit more again then that will be what I will like and what we will need as well. I think that was a great advert for Kenilworth Road for when it’s at its best.”
Luton have not played in the top flight since being relegated from the old First Division in 1992 – the year before the Premier League was launched – and they even dropped out of the Football League in the intervening period.
However, after finally escaping the Conference following a five-year exile in 2014 they have enjoyed a remarkable rise and, if they can overcome Sunderland, they would be one game away from a return to English football’s top table.
Defender Amari’i Bell, whose side were unbeaten in 14 games going into the first leg against Sunderland, said of the return meeting with the Black Cats: “I think it’s the biggest game of most of our careers.
“We’ve got to go out there and give it our all. I think everyone’s excited, looking forward to the challenge and relishing the position we’ve put ourselves in.
“The last loss was a long time ago and we forgot what it’s like to lose. It’s not something we’re used to but we know we have to bounce back and normally when that happens (lose) we do, so it’s going to be a good tie.”
Luton eye promotion to the Premier League for the first time and a win over Coventry would round off their fourth promotion in 10 seasons.
Manager Edwards refused to romanticise the club’s journey and highlighted the importance of a grounded mentality ahead of Saturday’s all-or-nothing showdown.
“I try and keep a clear head but I know the magnitude of the game and we all do, there’s no point in not talking about it, there’s nothing wrong with dreaming and aiming for (promotion), Edwards said.
“We are there now, in touching distance. It’s one game, we know we are capable.
“But the one thing we need to do is make sure we are the best version of us and prepare as normally as possible. We have to work as hard as we usually do, organise the same and if we get those bits right you stand a chance – the basics.
“If we get carried away then you have got no chance in a game like this so my job is to make sure we concentrate on the stuff we can control and we have to work as hard as we always do.”
Edwards heaped praise on Coventry, whose 22 clean sheets this season were the most of any Sky Bet Championship side.
The two sides met twice over the course of the season, drawing 2-2 in September and 1-1 in February.
“We have a decent idea of them and they have a decent idea of us as well, we’ve looked at each other twice during the season and watched countless numbers of games as well so there won’t be too many surprises on the day, said Edwards, adding that his side cannot just focus on Coventry’s star men Gustavo Hamer and Viktor Gyokeres.
“They have some more good players than just those two – who are excellent, they are top individuals.
“But they have got quality all over the pitch and really well coached by Mark (Robins) and Adi (Viveash) so they have got a real clear way of playing and that helps you over the course of a season.
“They’ve been building over a good few years and it’s served them well so of course they are more than two players, but you need outstanding individuals to make the difference and those two lads are the key ones this year.”
Edwards admitted the playoff final is the biggest occasion in his seven-year managerial career and understands the importance of victory.
“There’s not a comparable game I’ve been a part of with this level of interest and what it is worth financially and people watching, it is a new experience for me,” he said.
“I am pleased to have been involved in big games at big stadiums and our players have as well but me stood on the touchline, it will be a great experience.”
Dominic Calvert-Lewin fell to the floor as his loss of balance was aided by a push in the back from former Toffees midfielder Ross Barkley and, in the space behind him at the near post, defender Vitalii Mykolenko diverted Alfie Doughty’s corner past his own goalkeeper.
VAR ruled there was not enough in Barkley’s intervention to overturn the goal but Dyche was not happy.
“I don’t think I was any more frustrated than I normally am. I was more frustrated with the first goal and two hands in Dominic Calvert-Lewin’s back,” he said.
“You can say he’s gone down light, which he probably did, but I’ve seen penalties given for treading on someone’s toe.”
Jack Harrison equalised in the second half after goalkeeper Tim Krul allowed his low shot to escape his grasp but deep into added time Cauley Woodrow fired home in a goalmouth scramble following another corner.
“The game was a scrappy, awkward, ugly affair. They got the best side of it with two set-pieces – it felt like that type of game,” added Dyche.
“When we scored to get equal we had 15 minutes when we looked the side more likely but we conceded a soft corner at the end and conceded a goal from a bit of a ricochet.
“Fair play to them, they found their way through it and got the win.”
Luton boss Rob Edwards admitted not having a replay played a big part in their joyous reaction at the final whistle.
“It was a big reason for the celebrations at the end,” he said.
“It is a competition we value and want to go as far as possible. I’m so pleased for the lads.
“It will give us belief and confidence, you can see there is belief in this group of players. We are getting better.”
Woodrow played on with a suspected broken hand after Everton centre-back James Tarkowski fell on him but his resilience was rewarded with a first goal since August.
“I felt it crack, so I was in a bit of shock for a while,” the forward told BBC Sport.
“I’m really pleased with myself because I have been waiting a long time for a goal.”
The 28-year-old fell to the floor during their Sky Bet Championship play-off final against Coventry on Saturday and was taken to hospital after being carried off the pitch on a stretcher.
Lockyer has since undergone tests at the Cavendish Clinic in London and the club confirmed he will be able to join their preparations for Premier League football next season.
A statement on the Luton website said: “The Welsh international has completed all the necessary medical tests and observations to be allowed home for a period of rest before the start of pre-season training, which he will be fit to take part in.
“We would like to thank everyone for their messages of love and support for Locks, who has had a season to remember and proudly led the team out on Saturday, with his team-mates completing the job for him.
“We can’t wait to see you back home at the Kenny with that trophy in your hands, Locks!”
Saturday’s final went to penalties after Jordan Clark’s opener was cancelled out by Gustavo Hamer to finish 1-1 after extra time, but the Hatters secured top-flight football with a 6-5 victory on penalties.
Luton players held up Lockyer’s shirt throughout their celebrations and the captain posted an update on Instagram after the game.
He said: “Well not quite where I thought I’d be celebrating at the final whistle!
“I would just like to say a massive thank you to the amazing physios and doctors at Luton and Wembley for the swift and thorough response.
“A much scarier moment for everyone else than myself I am sure!
“Commiserations to Coventry a fantastic opponent over 3 games which had to be decided by penalties.
“I am currently in hospital under precaution and will stay here overnight for further tests in the morning.
“I am feeling very much myself, helped by the way the lads left it all out on pitch! It’s such an honour to be part of this team.. Premier League baby.”
Lockyer suffered a cardiac arrest during Luton’s Premier League game at Bournemouth in December and his heart stopped for two minutes and 40 seconds.
The 29-year-old was saved as medics rushed to perform CPR (Cardiopulmonary Resuscitation) and provide early defibrillation.
Wales defender Lockyer has since supported the British Heart Foundation’s campaign for people to learn CPR skills, as well as raise funds for lifesaving research.
“The medical team came in and we did the class,” Page said of his squad undertaking a CPR and defibrillator training course in September that would take on special significance three months later.
“Tom is championing it at the minute, and rightly so.
“It just shows that there’s more to life than football.”
Lockyer returned to the scene of his on-pitch cardiac arrest on Wednesday for Luton’s re-arranged meeting with Bournemouth.
The 16-times capped central defender met medics who helped save his life and admitted that he “got a little bit emotional”, while describing them as “heroes”.
Lockyer has since been fitted with an implantable cardioverter defibrillator and conceded it is “out of his hands” if he will ever play again.
But he will be part of Wales’ preparations next week as they bid to qualify for Euro 2024 and a third successive European Championship.
Wales host Finland in a play-off semi-final in Cardiff next Thursday, with the winners at home to Estonia or Poland five days later to decide a place in Germany this summer.
Page said: “I’ve had a good conversation with Locks and he’ll be a part of it. We don’t know what days or for how long yet.
“But he’s keen to come in and we’re keen to have him around the lads.
“I can only imagine how hard it was for Meps (Chris Mepham), Kieffer (Moore) and Brooksy (David Brooks) when they played that fixture and saw their mate on the floor like he was.
“I can only imagine how hard it would have been for them.
“They’ve had contact straight after and they’ve been in touch since, but it’ll be nice to have them all back in the group together.
“Forget football, just being together as good mates is powerful for them.”