Videos went viral of Lampard's foul-mouth argument with the Klopp's staff during the first half on Wednesday evening.
The Blues manager was not happy with Liverpool being awarded free-kick for what he deemed a good tackle by Mateo Kovacic on Sadio Mane.
Lampard has no regrets about his passion but was not to pleased with the language he used at the time.
“To be honest, I have seen the video and I was there. In terms of the language I used, I do regret that," he said, according to the Mirror.
“These things get played a lot on social media. I have two young daughters on social media, but in terms of my passion to defend my team, then no [regrets].”
Lampard also refused to comment on Jamie Carragher's criticism of goalkeeper Kepa Arrizabalaga following the loss to the Reds.
“Don't want to comment on other people's comments about players. That's their opinion," he added.
“I have to work behind the scenes. My only thought now is how we approach two games domestically and then Bayern. That goes for every player, not just Kepa.”
