The Hoops defender is positive the 41-year-old coach will not abandon the club, despite threatening during a heated debate with fans that he is prepared to leave
Lennon's comments came after a heated argument with several supporters in the aftermath of Saturday's 1-0 defeat to Inverness at Parkhead. Lennon said he would "do the honourable thing" and go if fans were not happy with him.
Mulgrew, speaking ahead of Celtic's game against Hearts on Wednesday, insisted the Ulsterman will remain with the SPL champions and that his threat was only made in anger.
"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," Mulgrew told reporters.
"But I don't think the manager will be leaving, he is right behind the cause here.
"When things aren't going right the fans obviously care and it shows in the way they supported us in [the Champions League win over] Barcelona and in different games this season.
"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 shows what passion the fans have and the manager as well."