On Thursday evening, Tevez was arrested on suspicion of driving while disqualified, which carries a maximum punishment of six months in prison. The South American has not been charged and is due back at Macclesfield police station on Tuesday.
And clearly, Tevez's problems are not much of an issue for Mancini.
"It is his problem. Not ours," the Italian said. "But if it has this effect on him I hope the police can stop him every day. After this he scored three goals. I hope next Friday too."
Tevez also created goals for Aleksandar Kolarov and David Silva as City romped to their biggest win of the season.
The former West Ham striker now has 15 goals for the season, and Mancini wants Tevez to stay on the scoring trail.
"It is important that he continues to score because we need his goals in this period of the season, and also for the cup," said Mancini.
Less clear is Tevez's future. After ending his infamous stand-off over a proposed move to AC Milan in January 2012, there has been talk of an extension to a contract due to expire at the end of next season.
However, so frequently has Tevez spoken of his wish to return to Argentina, Mancini cannot be sure that signing the extension will happen.
"I don't know what will happen in the summer," said Mancini. "Carlos has another year on his contract but many times he has said he wants to go back to Argentina.
"It depends on him. At this moment we can say nothing. Our focus should just be on the last two months."
City are now in the last four for the second time in three years and still on track to become only the fourth team to win the FA Cup without conceding a goal, and the first since Bury in 1903.
And what Mancini regards as a "dream" final against Manchester United is still alive.
"It could be perfect because in the last two years United and City have been the best teams in England," he said.
Barnsley manager David Flitcroft could have no complaint at the outcome.
His Championship relegation scrappers were outplayed from the first whistle to last and in the end were lucky to get away with not conceding more.
"If they are the second best team in the country, I wouldn't like to have played Manchester United," Flitcroft said.
"They were ruthless. They battered us to a pulp at half-time and then come out in the second half and tried to drill us into the floor.
"That left a massive impression on me. It is what champions are about.
"They wanted to floor us. They wanted to get seven, eight, nine, 10 goals. At times it was a real slow death.
"The only thing is we won't come up against a force that is Manchester City again. You don't face that kind of power in the Championship."
And it is a fair bet, no-one like Tevez is there either.
"It is his power," said Flitcroft. "It is his explosion and movement. It is incredible.
"He is a ghost. We talked about getting close to him in the box but the players said he just pulls off defenders.
"Every shot is on target. He is brilliant."