But Edin Dzeko and Sergio Aguero struck in stoppage time to seal City's first title success in 44 years.
Belgian centre-back Kompany added: "We knew Manchester United were winning but always said we had to focus on our game. We knew we had to win.
How a dramatic final day unfolded in the title race
Wayne Rooney sends Man Utd two points clear at the top by giving his side a 1-0 lead at Sunderland.
Silence turns to bedlam at Etihad Stadium as Pablo Zabaleta puts Man City ahead against QPR back on top on goal difference.
Advantage United. Djibril Cisse stuns City with an equaliser and it is all change at the top again. Sir Alex Ferguson's side are two points clear with 42 minutes of normal time to go in the season.
City are capitulating. After Joey Barton is sent off for QPR, Jamie Mackie puts the Londoners ahead against all the odds. United, now three points clear with 24 minutes of normal time remaining, dare to dream.
90 + 2 mins:
Lifeline for City. Edin Dzeko levels for City but United are still leading and remain two points clear with just moments left.
90 + 5 mins:
Man Utd win at Sunderland but City are still playing. And City despair turns to delirium as Sergio Aguero scores a last-gasp winner. It is utter heartbreak for Man Utd's fans at the Stadium of Light, though, as news filters through of the late drama. Game over. City win title.
"This season has been unbelievable, so emotional, and when you do it like [we did] there are no words to describe how it happened.
"For all the club legends and fans who have waited so long, I'm so, so happy."
City midfielder Gareth Barry said: "I was fearing the worst with five minutes to go.
"It was a massive mountain to climb. It all fell perfectly, with QPR knowing they were safe and all of a sudden we were on a high."
Match-winner Aguero, who finished his first season with City with
30 goals in all competitions,
said: "The only thing I can say is I am really happy.
"The truth is we can hardly believe it ourselves.
"We thought the Premier League had gone. Thank God it all worked out for us.
"We got two goals in five minutes, it was absolutely unbelievable."
City striker Mario Balotelli echoed Kompany's sentiments that the club were rightful title winners as he also insisted he would be staying with the Manchester outfit.
"We are the best and that's why we won," said the Italian, who came on with the score at 2-1 against QPR. "We didn't play very well in a few games but the rest of season we played very well so we deserved to win.
"Personally I think too many people talked and too many people said bad things about me, and now they have just to shut up.
"Manchester City is a great club, a great team, I have great team-mates.
"I don't see my future far from here so I think I want to be here."
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