City have 12 games left, two more than Leicester, and head to Anfield to face Liverpool later on Wednesday after beating the Merseysiders on penalties in the League Cup final on Sunday.
"What we've learned in our recent history is that in moments like this, you just have to get your head down and start racing as much as you can. It's what we call the hunting season," Kompany, who led City to the title in 2012 and 2014, told the club's website.
"So we're not going to look back or do anything other than focus on the opponents that we have to play. There's no other way to approach this anymore. You can't come with mathematics or anything like this."
Fourth-placed City lost ground in the title race after back-to-back home defeats by Leicester and second-placed Tottenham Hotspur last time out but Kompany, whose side are also in the Champions League last 16, said nothing was lost.
"We still have a lot to play for but nothing to lose anymore. It's a weird feeling but, as I say, it is hunting season so it's better to be chasing than be chased in some ways," the Belgium defender said.
"The whole organisation - everyone at the club has to have the knife between the teeth and know that now everyone needs to be as sharp and focused as ever."