The France international was jeered ferociously throughout the game before reportedly being involved in a post-match spat with Emmanuel Frimpong.
The reception from the home support was something which Mancini believes may have affected Nasri's performance.
"He can play better because he is a top player," he said.
"Tonight is the first night he came back to Arsenal and it is not easy for a player that played here for four or five years.
"I think that he can improve a lot but it was the same situation with those who arrived last year, like Edin (Dzeko) and David (Silva).
"It (the win) is not important for him, it is important for the team. For him it is better than he played tonight so when he comes back to play here in the league he knows what will happen."