Lebese came on in the 22nd minute for striker Thokozani Sekotlong and was then replaced by Leonardo Castro in the 74th minute on Sunday.
As Lebese walked towards the Sundowns bench - evidently disappointed - Mosimane stopped him and gave him a quick word in the ear, explaining why he had to take him off.
Lebese has not found his feet at Sundowns since leaving Kaizer Chiefs.
Sundowns lost 1-0 and it means they will finish the calender year without a major domestic trophy in the cabinet.
“I apologised to George. You must also understand that it was an early substitution because Sekotlong could not continue. I apologised because I took him off. But when you look at the number of minutes, you sometimes do a sub when a player plays 50 minutes or 60 minutes," Mosimane said after the game.
"It does not look nice because he came in and came off, but I apologised and said 'you've got to understand why I am doing this because we are trying to score, so we need to increase strikers'.
"That's the way it is, it's life. These things happen. I told him that he must be strong and not think that his career is down. He has to understand it's part of football. He said he understands."
Sundowns have lost three matches in a row for the first time since Mosimane took over from Johan Neeskens in 2012.
"I am the leader. If I press panic buttons, then the players will also lose it. So you have to keep calm and you have to keep everybody calm. And you have to look at the game. Are we playing well? Yes, I think we are playing well. I don't press panic buttons because I look [at] what's happening and I understand what's happening."
Sundowns take on Orlando Pirates in the Absa Premiership at Orlando Stadium on Wednesday (19h30).