Words were exchanged between the Reds boss and the visitors' bench after the 2-2 Champions League draw at Anfield.
But Klopp said his part in the dismissal - when Berizzo threw the ball away from Joe Gomez for a second time at a throw-in - had nothing to do with him and the issue had been cleared up after the game.
"They think I had something to do with the red card of my colleague
I don't think I had a percentage of influence on this decision," he said.
"I was not happy with him throwing the ball away
I was not exceptionally emotional in this situation
He threw the ball away but I didn't send him to the stand.
"The manager of Sevilla asked me to come into the dressing room as he wanted to explain to me the situation of his red card
There were a lot of smiles on their faces."
Klopp was the one smiling least after a Dejan Lovren mistake allowed Wissam Ben Yedder to score just five minutes into Liverpool's return to the Champions League but goals from Roberto Firmino, who also missed a penalty, and Mohamed Salah appeared to have put them in control.
However, with 18 minutes to go the defence switched off and Joaquin Correa equalised and, to compound Liverpool's frustration, Joe Gomez was sent off in added time for a second bookable offence.
Klopp was left to rue more defensive mistakes, a trait which has troubled him since he arrived at the club in October 2015, but insists there is no quick fix and rejected suggestions that the problem would have been eradicated had they signed primary transfer target Virgil van Dijk in the summer.
The Reds were forced to publicly withdraw their interest in the £65million-rated Dutch centre-back - who Southampton refused to sell - after a tapping-up row but the boss said the issue was more complex than that.
"I know you are always looking for this thing - the defence was always something being talked about: 'We didn't sign this or that'," he said.
"If these problems could be solved by one player you can imagine we would have put all our money into it and say: 'Let's do this'.
"It is about being dominant and losing a bit the grip on the game that you are not in all the defensive moments.
"There is space for improvement
We need to learn to be dominant and not give easy goals.
"It is disappointment, frustration, but that is completely normal
We are responsible for the very good parts in the game and also the not-so-good parts so you have to feel disappointed after a game like this.
"It is not a general defending problem but we have to improve 100 per cent."
Sevilla coach Berizzo admitted his sending-off was all his own fault.
"When we were winning and Liverpool were on the counter I did something that wasn't right, I threw the ball to stop the advantage of a counter-attack
I realised that was a mistake," he said of his first offence.
"However in the second half, when we were losing and chasing the game, I still decided to throw the ball away to make up for (my actions in) the first half so I tried to do the same.
"Klopp understood but the referee didn't understand, he was the only one.
"I had a chat with Klopp and wanted to put right the initial mistake
He (the referee) did act to the letter of the law, but I wanted to try to explain.
"What I did explain to the Liverpool staff is that it wasn't a bad intention, I was just trying to make up for what happened before."
Source : PA
Source: PA