The Serb moved to San Siro from Manchester United in the close-season but his competitive debut against Torino did not go according to plan.
Vidic gave away a penalty, which was subsequently missed, before being dismissed in second-half stoppage time for sarcastically applauding referee Daniele Doveri.
After missing Inter's 7-0 thumping of Sassuolo through suspension, Vidic is back in contention for the trip to Palermo on Sunday, and the 32-year-old admits he will have to be careful in his actions in the future.
"Obviously I have to adapt," he said.
"I am still learning the way I have to play in Italian football and that includes the referees, the way they manage the games and hopefully I'll do that as soon as possible.
"To be fair, I believe the referees have a hard job because the players sometimes try to make situations happen, asking for penalties or fouls. I have to say in England they didn't do that as much as here, so it's difficult for referees.
"I have to adapt to not just the referees, but also the way they play here. I spoke to the club and they explained the things I shouldn't do here and what will get me punished. I don't want the team to risk bad situations here.
"If you ask me what I prefer, then that's to play the way I play in England, as I believe it's more honest and respectful.
"Sometimes these situations can happen to you and sometimes to your opponents, but neither way is good. I am here to adapt, not to change the mentality."