Tevez has been frozen out of the first-team picture since Mancini claimed the Argentinian refused to play in the Champions League loss at Bayern Munich on September 27.
Mancini was quoted on Tuesday in an Italian newspaper saying he would welcome Tevez back from his current isolation if an apology was forthcoming and reiterated his thoughts at a press conference on Tuesday evening.
Speaking ahead of Wednesday's Champions League game at Villarreal, Mancini said: "We are here to talk regarding the game.
"I said only my opinion. In life everyone can make mistakes but it is important to apologise in every situation.
"These are the crucial words, these easy words, when you make some mistake in life."
It is the first time Mancini has spoken significantly on the matter since the night in question five weeks ago.
After an exhaustive investigation, City last week found Tevez guilty of refusing to play and four other breaches of contract.
He was fined four weeks' wages, although that was later reduced to two following intervention from the Professional Footballers' Association.
Tevez is still thought highly likely to appeal against the verdict having contended throughout that he only refused to warm up.
Press Association Sport also understands the 27-year-old is considering suing Mancini for defamation of character over his post-match comments.
Representatives for Tevez, who still have a week to formally announce whether the player will appeal, chose not to comment on Mancini's latest remarks.
Tevez has blamed a "misunderstanding" for the whole fiasco and did apologise to supporters for that the morning after the game.
Without Tevez, City secured their first win in the Champions League with a last-gasp 2-1 victory over Villarreal at the Etihad Stadium a fortnight ago.
Mancini feels that late Sergio Aguero winner has changed the complexion of Group A heading into the final three games.
City now have four points and are just three behind group leaders Bayern and two below Napoli.
Mancini said: "That goal was really important. It is not easy to play against Villarreal.
"They are a good team, used to playing in the Champions League.
"Also when they played against us in Manchester they did very well.
"Many top teams have played at El Madrigal and had big problems.
"The supporters are very close to the teams and Villarreal when they play at home are a strong team.
"For this reason I think tomorrow [Wednesday] will be a tough game. If we want to win we must play a very strong match."
City's European form has not been as eye-catching as their domestic progress with Mancini's side five points clear at the top of the Barclays Premier League.
But even though he boasts a star-studded squad, several of whom have Champions League experience, Mancini does not feel that should be a surprise.
While his team have now been installed as Premier League favourites, Mancini is keeping ambitions for the Champions League relatively modest.
He said: "It is the first time in the Champions League for us and we would like to go to the second stage. It is the first time as a team.
"The first games against Napoli and in Munich were difficult, and the same against Villarreal.
"The Champions League is good for this - every game is hard.
"It is harder than the Premier League. It is a difficult tournament, a very strange tournament.
"Tomorrow [Wednesday] will be the fourth game and I hope we can do better. The target is to go into the second stage."
Morale is certainly sky-high among the squad with 36 goals scored in just 10 domestic league games but Mancini will not allow his players to relax.
He said: "We are top of the table, we can play Champions League.
"The squad is a good squad but if we want to stay at the top for a long time we need to improve.
"We need to continue to work hard but now we have good confidence."