The 26-year-old striker has scored three goals so far this season, after netting 29 goals in all competitions during his maiden campaign for City.
And while he did not expect to be handed the captaincy by manager Roberto Mancini, the Argentina international is relishing the role.
He told The Guardian: "It did surprise me. For one thing, my English isn't fantastic and communicating in the dressing room isn't always easy.
"But it's certainly having a positive effect on my game. Before maybe I would disappear from games for 10 or 15 minutes, but now I can't afford to do that. I've got to concentrate 100% all the time."
Mancini's decision to give the armband to Tevez was considered a surprise following the player's criticism of his manager's training methods towards the end of last season, but the former West Ham and Manchester United forward has no regrets about speaking his mind.
"I think I was right to say that," he continued. "This season, because the games are coming so thick and fast, there isn't time for double training so I am relieved it's not an issue. But I still stand by what I said.
"Roberto and I had a good chat at the end of last season and everything was left really nice. It was simply two guys sitting down in a room and chatting honestly and openly and sorting things out."
Tevez admits he came close to signing for Chelsea when he left Manchester United.
The Argentine ace admits he could have been playing for Chelsea instead of Manchester City after holding talks with Blues boss Carlo Ancelotti prior to his switch to Eastlands.
"When Man United didn't want me, I had a conversation with Ancelotti but there was never any concrete offer," revealed Tevez.
"I only ever talk about proper, written offers - and that was the case with City."
Tevez also spoke of his disappointment that Craig Bellamy has been allowed to go out on loan to npower Championship side Cardiff, saying the Welshman's presence is missed in the Eastlands dressing room.
"I was disappointed when Craig went and I still feel sad about it. Craig really feels football.
"Along with myself and Shay Given, he was always up for fans' awards and you could see why. We combined well and he was good to have in the dressing room, so it's a shame."