City edged neighbours Manchester United 2-1 at Old Trafford thanks to a late goal from Sergio Aguero and Kompany, whose own-goal got the Red Devils back on level terms early in the second half after James Milner's opener, was thrilled for the fans.
"The derby is always a special game and for us to win this game is massive," he told Sky Sports 1. "Our fans are still celebrating and it's a great night for us.
"I think we all worked very hard. They played very offensively and have an unbelievable strike-force. We had to close the gaps and had to be tight to them. We did that.
"I don't think we gave a lot of chances away and if you look at the overall play I thought we were the better team, and we're very happy."