The Belgium international scored the winner in the crucial derby clash to put his side top and give Roberto Mancini's men momentum heading into the final two games of the season
The Belgium international's first-half header was enough to secure City three points, which sees them leapfrog United into top spot in the Premier League, but only on goal difference.
City will clinch the title if they secure maximum points from their trip to Newcastle United on Sunday and their final game of the season against QPR at the Etihad Stadium.
Kompany told Sky Sports: "I'm absolutely buzzing. We've been waiting for this moment for a very long time. It's far from over and we know that but just to give our fans two wins over Manchester United this season – we have to finish it off and I hope we can show it over the next two games.
"I know that a lot of predictions go wrong but I remember someone texting me and saying 'you're going to score the winning goal'. I thought he was a lunatic."
The City captain saluted the dominant display from his team-mates and revealed that the club's chairman, Khaldoon Al Mubarak, had spoken to the players prior to the victory on Monday evening.
"The victory is for the whole team, the performance was great. I heard I'm going to get man of the match, but for me it's for all the players, there were so many great performances and I'm happy for them," Kompany said.
"The chairman came in today and had a word with the players. He said 'no matter what the result today we're proud of you guys, you've played great this season and we're building for the future'. So for us to get this result is just a bonus and we wanted it so bad.
"So much has been said about it but it's all about football. It all comes down to the dreams we had as children and that's what we want."