The Premier League leaders failed to match Leicester's valuation of the player, understood to be near the £80 million mark, and talks collapsed on the final day of the January transfer window, with Mahrez having submitted a transfer request.
The 26-year-old started on the bench and was introduced on the hour mark as Man City beat Leicester 5-1 in the Premier League last weekend.
'For me, it's important.
Mahrez spent several days absent from the club, following the well publicised breakdown of his proposed move to Manchester City on transfer deadline day at the end of January. "We need to manage better and we need also perhaps some respect from others".
Mahrez is now pushing for a recall to Leicester's starting line-up on Friday night when they host Sheffield United in the FA Cup.
But speaking at a news conference ahead of his side's FA Cup tie at home to Championship side Sheffield United on Friday, Puel, asked whether Mahrez was training as well as before, said: "I think better".
'I can not suffer this situation because other teams make this thing against us.
"It was important to stay united within the club, the fans, the players, among themselves". 'Riyad gave his feeling in the dressing room, the details will remain inside the club, ' Puel said.
"He enjoys to play and train with his team-mates and he is at a good level with no problem".
'He has come back with a smile. They welcomed him with a good feeling, now it is important to move on.