Roberto Mancini's side proved they can go toe-to-toe with the Premier League's best following a 1-0 success over red-hot Chelsea on Saturday.
However, the win has only moved City within four points of the leaders having lost against Sunderland and dropped points in games with Blackburn and Tottenham.
Tevez feels his team-mates raise their game against the big boys and that, in order to take their form to the next level, they need to improve their intensity and concentration against the weaker teams.
"We always play very well against the big teams but the important thing now is we concentrate and play the same game against the smaller teams," said Tevez.
"If we can do that it will take us to the next level."
Tevez felt City's win was crucial in the Premier League title race and scoring the winner against Chelsea made the occasion even more special.
"This was a great result in the battle for the Championship. It was really important we won.
"I like playing against most teams but seem to make a special mark against Chelsea.
"We are becoming a strong team and as captain it's important I give them the strength and spirit to continue this way."