Kompany has also refused to blame the missed opportunity to sign Robin van Persie for United's nine-point advantage.
Van Persie was pursued by both Manchester clubs last summer but opted for United and his 22 goals so far - including a last-minute winner in the first Manchester derby - have helped Sir Alex Ferguson's men build a healthy advantage with 13 matches left in the season.
City might sense their title slipping away but Kompany is not giving up the fight.
"Nothing matters apart from being first," he told the Daily Mail. "Anything below that then you are just another top team that's failed.
"We are not about to give up but the reality is that we are up against a very good United team."
Questions have been asked about how much City improved - if at all - during a frustrating summer transfer window, with Van Persie's move to United just one of a number of disappointments.
"United hit the jackpot with Van Persie," Kompany added. "But you can't think "What if" about Van Persie. I am not sitting here thinking, "What if we had signed Lionel Messi" either.
"His transfer has made a direct impact but to say he's the reason we can't make it - if it turns out that way - is not correct. I still believe we can do this but if we don't, there will be plenty more reasons than the fact we didn't sign one player and another club did."
Kompany has missed a number of recent games through injury, but at least avoided a three-match suspension when his red card for a tackle on Arsenal's Jack Wilshere was overturned.
The 26-year-old Belgium international believes it is vital for the English game that tackling is protected and the game does not go the way of other European leagues.
"It's the way the game is played here that makes it possible for fans from all around the world to watch it on TV," he said. "The intention of what you do - if it's wrong - should be punished severely. I'm clear on that. But let's not ruin the game."