Ehiogu, who was Tottenham's Under-23 coach, died in the early hours of Friday after suffering a cardiac arrest on Thursday morning. The former England defender was 44.
Spurs are four points adrift of leaders Chelsea in the league, and face Crystal Palace at Selhurst Park on Wednesday.
Kane said: "Of course, we'll do everything we can to win the league for him.
"Of course the last couple of days have been tough.
Ugo was a great character around the training ground, and it was just shocking news.
"But that is no excuse for what happened against Chelsea, as we still had a job to do.
"I thought we did very well and probably deserved more but when you play the big teams on the big stage you need those big moments to go your way they didn't.
"We wanted to win for him and for ourselves as well. There are still six tough games left in the Premier League.
"We can't control what Chelsea do now.
"We just have to win as many as we can and it starts Wednesday with a tough game away at Palace."