Tevez, who joined City in the summer after United decided not to spend £25million to keep him, goaded former United team-mate Gary Neville during his two-goal performance in the 2-1 Carling Cup semi-final first-leg victory. Neville publicly backed Sir Alex Ferguson's decision not to buy the forward.
The Argentina striker also gestured towards the United directors but insists there was "nothing malicious intended".
"Gary was very disrespectful, which is out of character, but he didn't know the whole story of why I left Manchester United and I believe I deserved his respect," Tevez said.
"Football is a form of theatre and it was just a form of banter. There was nothing malicious intended. I was not trying to incite anyone but I was entitled to say to Neville that he should have been more respectful.
"For the second goal I ran to the touchline and cupped my ears and looked up to the part of the ground where the United directors were sitting, and also to Ferguson in the dugout, because I wanted them to know this was my response to them saying I was not worth the money.
"People from United have been speaking about me publicly and criticising me but I wanted to do my talking on the pitch because that was the best way of responding to all these people, such as Neville, who were saying United were right to let me go."