The Premier League leaders were looking to push a £60 million deal through before the deadline, but were met by stubborn resistance from the Foxes - despite Mahrez asking for a move.
And boss Puel has now questioned the timing of the offer that saw Mahrez go AWOL from training and miss two Leicester games.
For some other teams, it is not a difficulty to replace their players.
It is unknown whether Man City will return in the summer.
"We had some solicitation from another club".
To make solicitation just one or two days before the end of the transfer window, I don't know if it is normal, said Puel. "I think it is important now to put an end to the talking about Riyad".
Puel said: "We need perhaps some others' respect".
Mahrez made his return in Manchester and when asked about how he might be received back at the King Power Stadium, Puel replied: "I think it was good reception when he came on against Man City".
"It was a situation behind us, it was important Riyad gave his feeling in the dressing room, the details will remain inside the club", said Puel.
"He came with the squad at the weekend, he travelled with the squad, it was important for him that he came with us to stop this situation".
"They welcomed him with a good feeling, now it's important to move on. We succeeded to keep united within the team".
Leicester ousted the Blades from the Carabao Cup back in August and Puel has urged his players to shrug off a heavy loss last time out and focus on their "good possibility" to reach the quarter-finals.