Tevez withdrew his transfer request hours before City's defeat to Everton.
Cahill told talkSPORT: "I'm very happy for Manchester City to keep a player like Tevez at the club because he's one of the best players in the world and to keep him in the Premier League is an achievement.
"It's hard because he's a very influential player, not only to this team but to all of the teams he's played in so he carries a lot of weight.
"The good thing is you see the effort that he put in today and you know he just wants to play football.
"The best thing for us was for Carlos to play because if he didn't then they [City] would say 'well Carlos didn't play so you didn't deserve the win'.
"I'm happy for the football club that they've kept their man and someone who's very influential to them"