The pair clashed at the Stadium of Light with the Black Cats boss also feeling the Reds were lucky to win the game
Lens was booked for a foul on Mamadou Sakho during the closing stages of Liverpool's 1-0 Premier League victory on Wednesday.
Klopp was unhappy with the challenge and felt Lens should have been sent off at the Stadium of Light.
Allardyce hit back at Klopp and said referee Kevin Friend had taken the appropriate action.
"If he thinks that's a red card, then he's a soft German. It's a yellow, a foul," he told reporters. "There was some foul and abusive language towards my staff that I didn't like."
Allardyce was responding to the former Borussia Dortmund coach's claims the tackle was definitely worthy of a red card.
Klopp said: "Of course. This is a foul. That is not allowed. For me that is a red card, finished."
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Allardyce said he had moved on from the sideline exchange with a handshake at the end of the game but did admit he felt Liverpool were lucky to have taken all three points.
"It was a cruel goal, very cruel indeed," Allardyce told the club's website.
"I don't think Liverpool created the goal. It was pure luck. Even the finish was slightly mis-hit, but it went in and that's what matters.
"I think that killed the whole place because we were so optimistic about the second half after what we'd tried to do in the first.
"It took a while to recover from that but in the end there wasn't enough quality play in the final third from ourselves to create the sort of chances to get us back in the game."