Erik ten Hag's first season in charge has been one of progress and, for the most part, positivity, with the side finishing third in the Premier League and sealing a Champions League return.
The Dutchman is only the second manager in United's history to win a major trophy in his first season and has the chance to add to February's Carabao Cup triumph.
Ten Hag's Red Devils head to Wembley for the first all-Manchester FA Cup final, when they will attempt to add to their cabinet and stop rivals City's attempts to win the treble.
"We have to recover well and start to prepare for the game," De Gea said. "Of course, we know it's a big final, a special game.
"We've been the whole year fighting to be in that position to win titles and we will try absolutely everything to try to win."
De Gea and his team-mates were all in at Carrington on Monday morning, with Sunday's starters focused on recovery from the 2-1 comeback win against Fulham at a bouncing Old Trafford.
Kenny Tete had put the visitors ahead in the Premier League season finale and Marco Silva's men would have extended their lead had Golden Glove winner De Gea not stopped Aleksandar Mitrovic's spot-kick.
United kicked on after that, with Jadon Sancho and Bruno Fernandes completing a victory that saw them beat Newcastle to third spot.
"We concede the first goal from a corner and then I think five minutes after we concede a penalty," De Gea, whose contract has yet to be extended beyond the summer, said.
"I was very positive. I was feeling like 'come on, you have to save this penalty, we have to finish properly the season at home, we have to win'.
"Then I make the save, everyone was happy, enjoying and I helped the team to win the three points today.
"The manager wants us to be focused every game, winning every game. Before the game he was shouting before 'come on guys, we have to finish properly, winning mentality'.
"So, yeah, we showed it again. 1-0 down, suffering a bit, but then we create chances and could have scored even more than two.
"But, like I say, a big way to finish the season with a victory and (it) gives a bit of enjoyment to the fans."
The result saw United equal the club's record of 27 home wins in all competitions in a single campaign, while also meaning they finished 17 points better off than last season.
"100 per cent, for sure, the improvement is there," De Gea told MUTV. Of course we still have a gap to improve but, yeah, a massive improvement from last season.
"Winning a cup, finish third - it's never easy to finish in the Champions League places in England.
"And then we have another final, a big final, so I think at the moment it is a great year."
As for Fulham, the defeat at Old Trafford was frustrating but this was a season to cherish having finished 10th on their return to the top-flight.
Goalscoring right-back Tete said: "Unbelievable season, every single player.
"If you saw how we fought all season for every single point. Not even one game was easy for us.
"I am just proud of the boys. We said it as well to each other and this is something we have to build on.
"We know now what our standard is, we know now what we can bring. I can't wait for next season."