City's 2-0 win at Crystal Palace and Liverpool's 2-0 loss at home to Chelsea put the league title in the hands of Manuel Pellegrini's team.
Kompany said it was a long way from being over – City are third and three points adrift of leaders Liverpool, but have a game in hand and a better goal difference.
"It is difficult to predict the outcome of this league," the Belgium international said.
"You would be crazy to think it is over, but obviously we did our job. It's in our own hands and you can't do more than that.
"There have been so many swaps and changes over the season, we are still very calm.
"By definition, I think we are the team in the league that can't ever give up - especially after the year we won it.
"We just kept our heads down. We knew we didn’t play to well and had to change it - the last two games have been good.
"Ultimately it's about the last straight and we seem to pick it up at the right time."
City finish their league campaign with clashes against Everton, Aston Villa and West Ham.
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
