Klopp's team saw their 14-game unbeaten Premier League run come to an end with the shock defeat at the Liberty Stadium on Monday.
The German said he had reacted to a fan goading him during the clash, which was settled by a 40th-minute goal from Alfie Mawson.
"He was shouting at me all the time," Klopp said.
"Sorry, I reacted one time, I remind myself I am a human being and not a professional manager who takes that all the time and they can say whatever they want.
"At one point, I said 'please'. I had not a recorder like you so nobody taped it, nobody could hear what he said. That's fine. That's how it is. I have no problem with that.
"I just had one moment where I thought 'now, that's enough'. I'm not sure if we were already 1-0 down, I think we were, but it had nothing to do with it, but only enough."
Liverpool were left in fourth in the table, three points behind third-placed Chelsea.
Klopp said his response to the fan was nothing bad, but admitted he should not have reacted.
"I'm sure I'm not the first manager. I think he's a season-ticket holder," he said.
"It's my fault as well; I shouldn’t have reacted. But I didn't say anything bad, only that I showed I wasn't too happy by what he was saying all the time."