Wellens appeared to take a dig at Postecoglou after defeat to Stockport on Saturday.
Asked whether injuries had played a part in the loss, Wellens said: "I'm not going to make excuses, I'm not Ange Postecoglou."
Wellens, however, later in the evening said: "After today's game, I was asked about the injuries within our squad and, without thinking, I made a stupid comment about Tottenham Hotspur.
"That comment was brought to my attention later in the evening and, having watched my interview back, I am deeply embarrassed and regret what I said.
"At Leyton Orient we have a strong relationship with Tottenham Hotspur and it was never my intention to say anything that would jeopardise that. Their manager, Ange Postecoglou, is a world-class coach and I want to apologise for my comments and wish Spurs all the very best for the second half of the season."
Leyton Orient have Spurs pair Jamie Donley and Josh Keeley on loan until the end of the season.