Lennon became engaged in a heated debate with a number of supporters during and after their 1-0 home defeat to Inverness on Saturday which led to him warning he may leave the Parkhead hotseat.
But speaking ahead of their game at Hearts on Wednesday, Mulgrew insisted the comments from Lennon and the fans were born of frustration.
"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," said Mulgrew.
"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."
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