The pair interacted with each other on a number of occasions during the feisty 2-2 Premier League draw at Anfield and Klopp did not exchange the customary handshake with his opposite number.
Speaking immediately after the match, Klopp said he had not shaken hands because “it was not a friendly game” and also criticised West Brom‘s style of play.
Pulis clearly was still stewing over the incident when he spoke to the media on Friday and argued Klopp’s criticism was to deflect attention from the Reds’ failings.
The Welshman said: “‘We apologise. We actually played three longer passes in 99 minutes than what Liverpool played in that game.
“But if I had a team that was worth £200million, playing against a team that was worth less than £20million and we never won that game, I’d be doing my best to divert it away from the fact that I had 10 times more value on the pitch than my opposition and couldn’t win.”
Klopp learned of Pulis’ comments just before his press conference ahead of Sunday’s clash with Watford but chose to extend an olive branch.
The German insisted he had simply forgotten to shake hands in the heat of the moment as he went to his players to celebrate their late equaliser and thank the fans.
Klopp said: “I can easily say sorry for everything I said during the game because I am very emotional, I think Tony Pulis is similar, and there were a few words. We were very close together.
“For me it was not a big problem but it was very intense and after the game I wanted to go to my team. Really I forgot to shake hands. That’s all.
“If we meet today, it would be no problem to say sorry and to shake hands, to have a talk about whatever. I have big respect for his work, no doubt about this.
“In that situation it was not easy to switch on the lamps and switch them off.”
On his comments after the match, Klopp added: “It was not a game where five minutes were enough to come back to a normal situation.”
The 48-year-old, though, denied the relationship with other managers is more heated in the Premier League than the Bundesliga.
“Only the coaching zones are closer, that’s the only difference,” he said. “We are all emotional and best friends in the league. We talk completely normal before the game, we ask about our families after the game and during the game.
“We are coaches of different teams and we say things you never would usually. That’s how it is on the pitch. But it was not that serious.”
WATFORD vs. LIVERPOOL