Villa were 5-0 up from a resounding win in Edinburgh last week and completed formalities in the second leg as first-half goals from Jhon Duran and Leon Bailey put them out of sight.
Substitute Matty Cash sealed a 3-0 win on the night as Villa hosted European football for the first time since 2010 and they now await Friday’s group-stage draw in Monaco to learn who they will face.
Four-time Europa League winner Emery said: “Yes of course (I’m happy). We finished it tonight.
“We needed to be in the group stage and we have to be happy and enjoy it with our supporters.
“Today it was a full stadium and to finish and qualify was fantastic. I’m really happy because I really enjoy it in Europe and I want to enjoy it now with Aston Villa.”
The Spaniard is expecting Villa to complete the loan signing of Clement Lenglet before the transfer window closes on Friday.
“He’s not completely signed, but he’s close to signing with us,” Emery said.
“He’s a player who can help us. With the injury to Tyrone Mings, he can replace him in the squad.”
Emery said it “was possible” that Philippe Coutinho could leave Villa Park on deadline day and added: “I’m very happy with our squad.
“The club made a big effort to complete our squad. There’s still one day to go and we’re going to be ready.”
Hibs are going through a difficult spell having sacked manager Lee Johnson on Sunday after a home defeat to Livingston had left them bottom of the cinch Premiership without a point.
They were outclassed for large periods in both legs against Villa, but were given a rapturous send-off by their noisy 2,200 travelling fans and caretaker boss David Gray said he was proud of them and his players.
Former Hibs defender Gray, appointed caretaker for a third time after Johnson’s departure, said: “I’m proud of the players.
“They worked right to the very end in difficult circumstances all round at the football club at the moment, but I can’t fault the effort or commitment from the players.
“Playing against this level of opposition, if you switch off for a split second or make a slight mistake, you get punished. They’re a top, top team with fantastic players.”
On Hibs’ impressive following, Gray added: “I’ve been at the club nearly 10 years now and they’ve always been fantastic.
“You say there was 2,000, I’m sure there was a lot more that came down. Fantastic support as always.”
Villa had lost back-to-back games to Newcastle and Manchester United but put that right against Forest to strengthen their grip on a top-four place.
Ollie Watkins and Douglas Luiz’s double saw them cruise into a 3-0 first-half lead only for Forest to scare them with goals either side of half-time through Moussa Niakhate and Morgan Gibbs-White.
But Leon Bailey struck on the hour to give Villa breathing space and they saw it out to give themselves a cushion over the chasing pack.
Emery said: “We were very excited and very motivated after we lost two matches at home after a long time in a row winning matches here, and feeling comfortable and strong and connected with our supporters and being confident.
“But after we lost two matches a home we could have lost a little bit of our confidence and could have lost something tactically.
“But we were planning the same matches that we played against Newcastle and Manchester United, even though we lost.
“We reacted well in Sheffield (United) and reacted well against Fulham and we were focused on getting confirmation we reacted well at home.
“Firstly playing with personality and second trying to control the game with our style. First half we did fantastically and I was very happy, I was feeling comfortable and confident.
“When they scored the goal it was the only chance we conceded in the first half and we started the second half with some doubt and they scored a goal but our reaction was fantastic as well, like we did before in other matches.
“After some doubt we reacted and were again playing with personality and trying to control the game.”
Nottingham Forest boss Nuno Espirito Santo was left to rue “a bad performance”.
Forest were overrun in the opening 40 minutes, but still found themselves back in the game with their goals either side of half-time.
They could not complete a comeback, though, as their poor start cost them.
“We started really, really bad, the beginning of the game was bad, it was too easy for the opponent to score,” the Portuguese said.
“We didn’t play well. A very bad first half, even though the goal gave us some hope, we started the second half really well at 3-2, we had a good chance for 3-3, the game was there for us.
“Then again a bad situation that put Villa 4-2 and it was game over. To sum up, a bad performance.
“That is something we are going to work on, analyse and try to understand why and try to understand if we can be better.
“I really believe we can do better – individually and as a team because it is too easy for the opponent to score.”
Since joining the Clarets from Bundesliga club Bayer Leverkusen at the end of the transfer window, Bailey has been used sparingly in the team’s line-up and is yet to start a match. Against Everton, however, he gave fans a hint of what could be in store for this season with a match-changing introduction.
Bailey entered the pitch in the 61st minute and had almost an immediate impact on proceedings. After Matty Cash’s thunderous shot put the hosts ahead in the 66th minute, Bailey’s viciously swung corner was headed into the back of his own net by Lucas Digne.
The Jamaican then got his first goal for Villa in fine style after sprinting on from the halfway line to a long ball provided by Danny Ings and crashing his shot into the net past a stranded Everton keeper Asmir Begović. Things, however, ended on a worrying note for Bailey who had to be substituted in the 82nd minute after going down with an injury. The change was later revealed to be more of a precaution.
“To have the fans chanting my name when I was going on, it was such an amazing feeling. Words can’t even explain. The fans were great tonight, it was perfect for me to get the goal for them tonight. I feel welcome as a Villa player,” Bailey said following the match.
“I was just excited to get on the pitch, and I delivered, it was a perfect night,” he added.
As for the injury, the player did not think it was that serious.
“It might have been from hitting the ball, maybe I hit it too hard. I just felt a little stiff in my quad, but I don’t think it’s anything serious. So instead of risking it, I just decided to come out instead of risking it. We have a lot of games coming up.”
