Klopp apologised for not shaking hands after last weekend's 2-2 Premier League draw, in which his team equalised in the sixth minute of added time, and for "a few words" exchanged with his opposite number during the game.
Earlier on Friday Pulis made a sarcastic "apology" of his own for "playing three longer passes in 99 minutes than Liverpool did".
He claimed that Klopp was trying to divert attention from the fact that his team was worth "ten times more" than Albion's but could not beat them, and added that West Bromwich were expecting a harder game this weekend at home to promoted Bournemouth.
"It wasn’t a big problem," Klopp told a news conference on Friday. "After the game I wanted to go to my team and be with them.
"Sometimes you do things in football you wouldn’t do in normal life but it wasn’t serious.
"Everything is different in those 98 minutes. I
can easily say sorry for everything I said during the game.
"I have big respect for Pulis' work."
He could not resist adding, however, of Sunday's game: "Their second goal was offside and a foul. Nobody talked about this. It was all about Klopp, Pulis and going to the fans."
The German confirmed that England international James Milner will miss Sunday's visit to Watford with a calf problem.
After taking only one point from two games, Klopp has also told expensive striker Christian Benteke to become more mobile.
"The situation is that as a striker if you don’t get enough crosses then you have to move more."
(Reporting by Steve Tongue; editing by Justin Palmer)
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