Premier League leaders City tried to sign Mahrez in the winter transfer window, but the Foxes stood firm and managed to keep hold of the Algerian international.
The 27-year-old was then absent from the team for a brief period but Puel says any fall-out from that failed move is now forgotten and he expects Mahrez to play a key role for Leicester in the remainder of the season.
"All that is finished," he told reporters. "It's behind us. He came back into the team with pleasure and is enjoying his football. There is no problem with this. We could see that in the game.
"He's our player and he will play for the team, like the other players. Now it's important to keep our focus for the remaining games."