The Red Devils beat Newcastle United 2-0 at Wembley in Sunday's final, and are still in with a chance of winning the Premier League, FA Cup and Europa League.
After the triumph in the capital, Weghorst was in determined mood to collect more trophies before his loan spell from Burnley ends.
"We win the first one now and still have three to go, so hungry for more," he said. "It's three left now. First one is in and first we have to stand still and enjoy it. But afterwards of course three to go. We have everything in our own hands so let's go."
The Dutch striker has scored just once in 10 appearances for United since his January arrival, but played a key role against Newcastle, providing the pass to Marcus Rashford, whose shot deflected in off Sven Botman to make it 2-0.
"It's a great feeling," he said. "For me not being here too long but for the club it's a long time ago we won silverware. It's good to have it back at the place where it belongs, to me. It's an amazing club."
Weghorst also admitted he "took a moment" at the final whistle, adding: "I can do really tough or I can do really cool, but for me this is a childhood dream; a childhood dream to play for this amazing club, to play a final and also be important in this final with the second goal.
"To give my all and then at the end if you win it you have to enjoy it because during the match you're only focused on one thing and that’s winning it and that's performing. After which you have to take a minute otherwise everything is passing by before you even notice and before you've enjoyed it."
Just days after humiliation at the hands of Liverpool, an unchanged United side responded fiercely to put one foot in the quarter-finals.
It was not all plain sailing for Erik ten Hag's side though, with Ayoze Perez equalising in the first half after Marcus Rashford gave the hosts an early need.
A strong second half put United in control though, as Antony guided home a trademark curler and Bruno Fernandes headed home to ensure a firm lead.
United came out of the blocks flying and, having already seen a Weghorst goal disallowed for offside, took the lead in the sixth minute as Rashford capped off a fine counter-attack to smash into the top corner.
Claudio Bravo was called into action to deny Weghorst and Rashford, before Betis equalised against the run of play when Juanmi clipped a pass to Leicester City loanee Perez, who drilled into the far corner and give David de Gea no chance.
Two minutes before the break, the visitors almost took the lead. De Gea sloppily gave the ball away to Juanmi, who fed a pass through to Perez, but United got away with it as his pass across the face of goal was deflected onto the post by Lisandro Martinez.
United retook the lead seven minutes after the restart, Antony cutting inside onto his left foot and curling beyond the reach of Bravo from outside the box.
The hosts' advantage was doubled just six minutes later, Fernandes finding space at the near post to head Luke Shaw's corner home despite Bravo getting both hands to the ball.
Bravo kept the scoreline respectable with a number of crucial saves but could do nothing as Weghorst tucked home on the rebound after Scott McTominay's effort was saved, with United on course for the quarter-finals.
The Liverpool forward was on target for the Oranje in the first half to cancel out Adam Buksa's opener, with Wout Weghorst then emerging from the bench to net a late winner and give Koeman's side a winning start to their campaign.
During the encounter in Hamburg, the Dutch registered 21 shots, their most in a game at a major tournament since 2012, but only four of those were on target, while their opponents managed seven from their 12 efforts, with both ending the contest with 1.26 expected goals (xG).
Gakpo was quick to highlight his side's wastefulness in the final third, explaining the players will analyse their performance and look to improve against France in Leipzig next Friday.
"It was a tough game against a tough opponent," Gakpo said. "Obviously, they scored first, so it was more difficult, but I think we created a lot of opportunities and some good chances, but we had to be more clinical.
"We have to analyse the game and see where we could hurt them more, then we have to take that into the next one."
Koeman echoed the thoughts of the Netherlands' number 11, saying: "I felt we should have been three or 4-1 up by then but if you want to win you must score goals, so we knew we needed to change something up front."
Weghorst's late contribution saw him score the fastest goal by a Netherlands substitute at the European Championships, netting the winning goal of the game just two minutes and 18 seconds after coming off the bench.
The Burnley striker, who spent the 2023-24 season on loan with Hoffenheim, highlighted the importance of the triumph, insisting all eyes are now firmly fixed on claiming a second Euros crown.
"It is so important to get the early win and for me personally, it's a dream scenario," the 31-year-old said. "I saw it coming and I felt the goal coming. Our aim now is to leave with the trophy."
Poland's winless run against the Netherlands continued, last beating the Dutch in 1980, but they started the encounter brightly when Buska headed home early on, becoming the fourth Poland player to score on his debut at the European Championships after Robert Lewandowski (2012), Arkadiusz Milik (2016) and Karol Linetty (2021).
The 27-year-old believes his side could have taken at least a point from the game, saying: "Of course the Netherlands were driving this match. However, we had a good few situations even after conceding the second goal, it's too bad that we are finishing this game with zero points.
"I have mixed feelings. First there was euphoria but now I'm just sad that we lost that match. We definitely played a good match against a really good team... No points in this case. However, we are not putting our guns down."
For footballers in Europe's top-five leagues - all of which have been postponed until at least early April - this is a good moment to look back on the season to date, assess what has gone right and wrong, and maybe put in a few hours on the treadmill at home.
There are some who have a little more to ponder than others.
Using Opta data, we've taken a look at some of the worst-performing players in their respective positions. Here, we examine those all-important personal-glory-hunters: the goalscorers.
We've analysed six key metrics when it comes to underperforming as a forward: shots off target, shooting accuracy, shot conversion rate, headed shots off target, big chance conversion rate and minutes per goal.
To make things more balanced, we've imposed some cut-off points, which are shown in the results below. These players have also been picked from those to make at least 10 league appearances this season, to make things a little fairer on those trying to mark a rare outing with a goal (here's looking at you, Phil Jones).
THE WORST ATTACKING STATS IN EUROPE'S TOP-FIVE LEAGUES 2019-20
BUNDESLIGA:
Most shots off target (Min. 30 shots): Robert Lewandowski(37)
Worst shooting accuracy (Min. 30 shots): Guido Burgstaller (32.14 per cent)
Worst shot conversion rate (Min. one goal scored): Matheus Cunha (7.14 per cent)
Most headed shots off target (Min. 5 shots): Wout Weghorst (16)
Worst big chance conversion rate (Min. 5 big chances): Guido Bergstaller(0 per cent, from 5)
Most minutes per goal: Robert Skov (624.33)
LALIGA:
Most shots off target (Min. 30 shots): Karim Benzema (40)
Worst shooting accuracy (Min. 30 shots): Jonathan Calleri(33.33 per cent)
Worst shot conversion rate (Min. one goal scored): Jonathan Calleri(3.33 per cent)
Most headed shots off target (Min. 5 shots): Joselu (15)
Worst big chance conversion rate (Min. 5 big chances): Sandro Ramirez (0 per cent, from 5)
Most minutes per goal: Jonathan Calleri (1362)
LIGUE 1:
Most shots off target (Min. 30 shots): Victor Osimhen (38)
Worst shooting accuracy (Min. 30 shots): Casimir Ninga (28 per cent)
Worst shot conversion rate (Min. one goal scored): Jonathan Bamba (2.7 per cent)
Most headed shots off target (Min. 5 shots): Victor Osimhen (14)
Worst big chance conversion rate (Min. 5 big chances): Kalifa Coulibaly (0 per cent, from 9)
Most minutes per goal: Jonathan Bamba (1941)
PREMIER LEAGUE:
Most shots off target (Min. 30 shots): Raul Jimenez (40)
Worst shooting accuracy (Min. 30 shots): Joelinton(36.36 per cent)
Worst shot conversion rate (Min. one goal scored): Joelinton(3.03 per cent)
Most headed shots off target (Min. 5 shots): Sebastien Haller (14)
Worst big chance conversion rate (Min. 5 big chances): David McGoldrick (0 per cent, from 15)
Most minutes per goal: Joelinton(2237)
SERIE A:
Most shots off target (Min. 30 shots): Cristiano Ronaldo (40)
Worst shooting accuracy (Min. 30 shots): Dries Mertens(33.33 per cent)
Worst shot conversion rate (Min. one goal scored): Suso(4.35 per cent)
Most headed shots off target (Min. 5 shots): Edin Dzeko (19)
Worst big chance conversion rate (Min. 5 big chances): Dries Mertens (16.67 per cent, from 6)
Most minutes per goal: Suso(1361)
AND THE TOP SIX:
Most shots off target (Min. 30 shots): Raul Jimenez (40)
Worst shooting accuracy (Min. 30 shots): Casimir Ninga (28 per cent)
Worst shot conversion rate (Min. one goal scored): Jonathan Bamba (2.7 per cent)
Most headed shots off target (Min. 5 shots): Edin Dzeko (19)
Worst big chance conversion rate (Min. 5 big chances): David McGoldrick (0 per cent, from 15)
Most minutes per goal: Joelinton (2237)
Substitute Wout Weghorst completed the turnaround for the Oranje late on, having gone behind to Adam Buksa's early effort.
The Poles would settle quicker than their opponents, and took the lead in the 16th minute as Buska rose highest to meet Piotr Zielinski's delivery into the box, the third consecutive goal the Netherlands have conceded from a corner kick, as many as in their previous 83 conceded goals.
Despite record top-scorer Robert Lewandowski watching on from the bench, he would have been pleased by his side's start to the contest as they aimed to secure their first win over their opponents since 1980.
However, Gakpo hauled the Netherlands level with the aid of a deflection from Bartosz Salamon, his effort bouncing over the helpless Wojciech Szczesny.
Both sides continued to exchange blows in their search for an important three points ahead of France's meeting with Austria in Dusseldorf on Monday.
But with seven minutes of the contest remaining, Weghorst emerged from the bench to score his seventh goal in his last 11 international appearances, finishing smartly after being picked out by Nathan Ake inside the box.
Data Debrief: Weghorst to the rescue as the Netherlands continue Poland streak
Gakpo's strike took him into double figures for his nation, and he has now scored in each of his last four group stage games at the European Championships and World Cup, becoming the third European player to do so this century, after Cristiano Ronaldo and Alvaro Morata.
Poland are now winless in their last 13 meetings with the Netherlands in all competitions (D5 L8), since a 2-0 home win in EURO 1980 qualifying.
