Tevez has informed the club that he wants to quit City for personal reasons as he wants to be closer to his family in Argentina.
The Argentina international submitted a transfer request in December, before quickly performing a dramatic U-turn and pledging his commitment to the club following clear-the-air talks.
However, Tevez is hoping to secure a move away from City this summer and Mancini admits he can understand the player's thinking and respects his decision.
Speaking to Sky Sports News' chief news reporter Bryan Swanson, who is with the City squad on their pre-season tour of USA and Canada, Mancini said: "When you talk about a player like Carlos, it's difficult because Carlos is a fantastic player, a good guy for me.
"Probably if we lose Carlos, we lose an important player.
"It is important that every player is happy to stay here or in our team, this is the most important thing for me.
"Every time I spoke to Carlos, he never said to me 'I want to leave'. He said he is missing his daughters, his family.
"I am very sorry if Carlos wants to leave because for me he is a good man and he's a fantastic player, but I respect his decision."
Brazilian side Corinthians are thought to be leading the chase to sign Tevez and they are believed to have tabled a new bid for the forward after seeing their initial bid rejected earlier this week.
Source: Team Talk
Source: Team Talk