The Leicester captain received a yellow card following an incident when he pushed his hand into Francois Hougaard’s face and appeared to pull the Wasps player’s hair.
The Tigers’ 16-13 loss on Sunday was their first reversal this season, ending a run of 11 successive Premiership victories.
Leicester flanker Tommy Reffell, meanwhile, received a yellow card earlier in the first half for an off-the-ball tackle.
“It potentially cost us the game, being down to 14 men for that amount of time,” said England prop Genge, who was making his 100th Leicester appearance.
“I think mine was an isolated incident with me losing my head for a split second off the back of someone doing something to me. Tommy’s was him working to get back to make a try-saving tackle. There was a big difference between the two.
“I’ve apologised to the boys for letting them down, I’ve apologised to Steve.
“It’s something I can’t promise I won’t do again, but it is one of those, you lose your head in the heat of the moment.
“I haven’t got a bad discipline record. I’ve never been red-carded in the professional game. I think I’ve got about four yellows in my professional career, so I guess that answers all your questions around that.
“For some reason I’ve got this weird perception that I’ve got bad discipline, I get peppered online about it. It goes in one ear and out the other. I feel like I probably let myself down.
“I am usually the one getting the reaction, as opposed to giving a reaction. It’s a learning lesson for me, being on the other side of the coin where I’ve lost my head in a split second.
“I’ve seen a lot of people saying I tried gouging him (Hougaard), which is absolutely ridiculous. I would never even dream of doing something like that. It’s disgusting.
“I lost my head, I pushed him in the face a little bit, I will learn from it. I’ve said sorry to the boys, I said sorry to Steve, and we move on.”
Borthwick appointed Genge to the role of skipper this season and he has played a pivotal role in helping Leicester reach the league campaign’s halfway stage with an eight-point lead at the Premiership summit.
Tigers also won their first two Heineken Champions Cup games last month and they appear well on course for a place in the tournament’s knockout phase.
Borthwick said: “He (Genge) is brilliant to be able to connect people – whether you are an 18-year-old coming out of the academy to someone with 100-plus caps, he can connect everyone together.
“If you’ve got someone who works hard, is brilliant with people and playing really well, he’s an incredibly powerful leader.
“From my point of view, the time I have worked with Ellis, he is terrific.
“He thinks calmly and is able to give clear instructions. He has grown to be a top-class international player.”
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