City came from behind to beat Liverpool 2-1, Kompany scoring the equaliser, at the Etihad Stadium this evening and lie just a point behind table-topping Arsenal.
And the Belgium defender told BT Sport: "The three points are massive, that's the hardest game so far. Liverpool are a good team so it's great for us.
"It's a weird (title race) because all the teams started a little slowly but now, I don't know how many wins we've had in a row but we can't grab that top spot."
Kompany enjoyed his battle with Premier League top scorer Luis Suarez and said: "I loved every single minute, I live for those games.
"After the game we had a handshake - he appreciates the battle, I appreciate the battle, we won but it was a tough game."
Liverpool boss Brendan Rodgers was unhappy both with the match officials and with his team's failings for City's two goals.
Having led through Philippe Coutinho, after Raheem Sterling had a goal disallowed for offside, the Reds were pegged back by Kompany before Simon Mignolet's error allowed Alvaro Negredo to score the winner.
Rodgers said: "Overall I'm very proud of the team, of how we played and the charisma in our football.
"We scored a wonderful first goal and I thought we could have had two or three more.
"I thought there were a number of incidents. The offside was incredible really, it was such an easy decision.
"I don't think we had anything that went our way today, so all credit to the players who kept going until the end.
"I'm disappointed we shipped a goal from a corner and for the second goal, we have to manage the game better coming up to half-time. That's an area we will look at, for sure.
"I'm disappointed to lose but the over-riding feeling is pride in my players."
Suarez was denied a late penalty after Joleon Lescott pulled his shirt while challenging for a corner, though Kompany was similarly manhandled by Martin Skrtel as he headed his goal.
And the City skipper said: "We would have liked to have penalties too, in the end I think the referee did the right thing.
"The game was tough, for soft fouls you should never give penalties."
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