Lennon said he would "do the honourable thing" and go if fans were not happy with him. The comments came after a heated argument with several supporters during and immediately after the Clydesdale Bank Premier League loss at Parkhead.
But Mulgrew, whose side take on Hearts at Tynecastle on Wednesday, said: "I think it is heat of the moment. Maybe they caught him straight after the game or whatever, with tempers running high it is something you say."
He added: "But I don't think the manager will be leaving, he is right behind the cause here."
Celtic were booed off after the defeat, which left them with one point from their last three SPL games at Celtic Park, where Barcelona were humbled earlier in the month in the Champions League.
"When things aren't going right the fans obviously care and it shows in the way they supported us in Barcelona and in different games this season," Mulgrew said.
"It is just heat of the moment and I don't think there is anything to be taken from it to be honest.
"Of course they pay their money and they come to watch the match, nobody says they can't have their views on what is happening.
"It show what passion the fans have and the manager as well."
- Sports & Recreation