The Argentina striker has scored four goals in his first two Premier League starts since ending a six-month dispute with City.
Tevez said: "We'll be fighting until the end and until it's mathematically impossible to be champions.
"We always knew United can lose points, and now they have to come to play at City which will be difficult.
"We won't give them any space. We are going to continue to put them under pressure, and then we will see how it finishes. The most important thing is to keep putting pressure on United. We have to keep playing the way we are and winning games."