A 52nd minute strike from former Barcelona man Yaya Toure broke the deadlock for City, who then held on superbly, aided by Paul Scholes seeing red and leaving Sir Alex Ferguson's charges with only 10 men.
Roberto Mancini's side were much improved in the second half having come under intense pressure from United in the first 45 minutes, and Dutch international De Jong has admitted that heated words were exchanged at the break.
He told The Guardian: "I won't give you the details but, obviously, everybody wants to win and sometimes you come face to face with each other. It happened in the dressing room and it is just a small thing.
"But it keeps the fire alive. Everyone wants to win the main prizes and we showed a great spirit in the second half. The belief has always been there.
"Obviously we've had our ups and downs and that's normal for a team that wants to progress. But in the second half we showed that belief. We came out of the dressing room and dominated United.
"We put a statement out there for the other teams but for the club as well. It's a big step forwards for us."
The World Cup finalist has also insisted that the club's season would still be seen as a failure if they were to end their 35-year wait for silverware against Stoke but fail to finish in the top four.
He said: “Everyone has been talking about City spending all this money and seeking out prizes, and now we're only one game away from winning our first silverware. For me, the guys are hungry but you've got to start somewhere in feeding that hunger. We did that against United.
"Now we must make a final push to take this club forward and make it happen. United have so many prizes but City is a big club as well. And now you have two clubs in Manchester dominating two of the competitions. History is a big part of this club but we are trying to change that history.
"But we just have to maintain our focus now. Our main goal this season was a top-four finish. This result will give us a big boost in confidence for the last six games of the season. We have to take a Champions League place because, otherwise, winning the FA Cup would all be for nothing.
"We can't just have one. We have to go for both. We can enjoy having reached the FA Cup final, but we have to focus on finishing in the top four too because we have important games to play."