The Algeria global had seen a proposed deadline day transfer to the Etihad Stadium collapse after the Foxes rejected City's offer.
Pep Guardiola's side are now 13 points clear atop the table while their opponents are sat in eighth.
Leicester, playing with five at the back and using Jamie Vardy's pace on the break, did not roll over and levelled when Nicolas Otamendi's mistake let the England striker in to score. He came off the bench in the second half against City. Congratulations to him because it's not easy to score four goals.
His second goal was a reward for his own hard work, closing down Kasper Schmeichel and forcing the keeper into a mistake before Kevin De Bruyne threaded a flawless pass in behind for Aguero to latch onto.
"Every time we dropped points this season, the next game we won, which is so important".
De Bruyne can challenge for Ballon d'Or, says Guardiola
Despite having the majority of possession in the half, Manchester City were failing to create much of anything in the middle. "If we are able to win the title it will be something special for us".
And Puel claimed both he and the Algeria global will focus their efforts on the rest of the season without any issues.
"The most important thing is that he came back to the training session, to the game", he told BBC Sport. "Now we need to look forward, to move on with all our best players".
Manchester City were linked to the 24-year old in the January transfer window, but they chose to buy Athletic Bilbao's Aymeric Laporte instead for a record £57.1 million.
But studio guest Shay Given felt it would be hard for Mahrez to regain his focus on the back of a hard few days for both the player and his club.
The tempo of the game was frantic from the very beginning, but City managed to control the possession well with their slick passing moves and intelligent off the ball running.