The Algeria worldwide had hoped to move to City on transfer deadline day but the move fell through as Leicester valued Mahrez at £95 million but City were only willing to pay £65m.
"He enjoys to play and train with his team-mates and he is at a good level with no problem", Puel told reporters ahead of the game.
"For some other teams, it's not a difficulty to replace their players".
According to Tidesports source, Man City's cash-plus-player offer for Mahrez was worth in the region of £65m, falling well below Leicester's valuation of around £95m for the deal.
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'For me, it's important. We needed to manage better and we need also perhaps some others' respect.
"We had some solicitation from another club", said Puel.
However, he made his Leicester comeback as a second-half substitute against prospective employers City last weekend just a day after returning to training as Puel's men were thrashed 5-1.
"I can not suffer this situation because other teams make this thing against us".
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"The game against Sheffield United will be tough, they are a good team".
However, Puel has been so impressed with the 26-year-old in training, he may even start the Foxes' FA Cup tie at home to Sheffield United. We have stayed united.
"It was a situation behind us".
"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. The story is behind him, all the players want to move on.
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A Tottenham spokesman was unavailable for comment when contacted by AFP in London. The 36-year-old Swede has not played for United since Boxing Day.
This comes after City failed to land the Leicester City player before the close of the transfer window last night.