Klopp’s men defeated Chelsea 5-3 in the Premier League at Anfield, thanks to goals from Naby Keita, Trent Alexander-Arnold, Gini Wijnaldum and Alex Oxlade-Chamberlain.
Lampard had clashed with Klopp’s assistant, Pep Lijnders, during the encounter, and later continued the row in his post-match interview.
He repeatedly told Klopp and his staff to “f**k off” and accused Liverpool of being “arrogant”.
Lampard said: “Some of the benches, it is a fine line between when you are winning, and they have won the league, fair play to Liverpool Football Club but also do not get too arrogant with it.”
Reacting to the development on Friday ahead of Liverpool’s Premier League clash with Newcastle United on Sunday, Klopp told a pre-match press conference when asked about the row: “You can’t hit me and my bench with something like that because we aren’t arrogant.
“Frank was obviously in a really competitive mood, and I respect that a lot. From my point of view in this sort of situation, you can say pretty much what you want. For me, after the game, it’s completely over.
“I said a lot in the past because it’s pure emotion. He came here to win the game or get a point, to make the Champions League qualification, and I respect that a lot. But what he has to learn is to finish it with the final whistle and he did not do that.
“Speaking afterwards about it like this, that is not okay, Frank has to learn this, and he has a lot of time to learn as he is a young coach, but that is what he has to learn.
“During the game, the words used were no problem at all but after the final whistle? No.
He added: “We are not arrogant, we are pretty much the opposite. But in a moment like this in an argument, you want to say something to hurt the other person. I have no problem with that but at the final whistle close the book. He did not do that, and that is what I do not like.”
