Speaking after the game, Lampard said: “Fair play to Liverpool Football Club, they’ve won the league, but also don’t get too arrogant with it.”
After Liverpool trained for their final game of the season, away to Newcastle on Sunday, Klopp revealed he was unhappy the former England midfielder chose to air his grievances after the match.
“You cannot hit me and my bench with something like that because we are not arrogant,” Klopp said.
“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 is completely over.
“But what he has to learn is to finish it with the final whistle and he didn’t do that. In a moment like this, in an argument you want to say something to hurt the other person.”
Klopp said Lampard could have chosen to “close the book” on the argument, but didn't.
“And that is what I don’t like,” he added.
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“Speaking afterwards about it like this, that’s not okay. Frank has to learn this and he has a lot of time to learn as he is a young coach. During the game, words used no problem at all but final whistle... we are not arrogant, we are pretty much the opposite.”
Lampard repeatedly used expletives to vent his anger at the Liverpool bench and, with Anfield being virtually empty because no fans are allowed, much of the argument could be heard clearly.
Lampard said on Friday he was sorry for his actions. “I think in terms of the language I used, I do regret that," he said.