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, 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."