Young Liverpool defender Joe Gomez was sent off in the dying seconds of the group game, the second 'dismissal' of the night after Berizzo had been sent to the stands on the hour for throwing the ball away after Gomez hurried to take a throw-in for the home team.
On the final whistle on Liverpool's return to the competition after two years, members of Berizzo's staff appeared to remonstrate with Klopp as the two benches walked down the tunnel.
"But I don't think I had a percentage of influence on his (manager's) position to be honest.
"I was not happy with him throwing the ball away but we're fine. He invited me into the dressing room and we spoke about it.
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"But in this situation I was not exceptionally emotional. It was an offensive situation for us, taking a throw-in, and somebody threw the ball away. But I didn't send him to the stand!"
Strangely, the Argentinian manager claimed he was wasting his own team's time to make amends for an incident in the first half when he had been warned by Dutch referee Danny Makkelie for a similar offence.
"I realised that was a mistake and in the second half, when the ball came to me and we were losing, I decided to throw the ball away to try and make up for what I did in the first half.
"I've had a chat with Klopp and explained exactly that I wanted to put right my initial mistake. He accepted that."
Berizzo could be satisfied with his evening's work after Joaquin Correa grabbed a late equaliser for the visitors.
Firmino and Mohamed Salah had earlier put the hosts 2-1 in front, cancelling out an early effort from Wissam Ben Yedder.
"Of course I'm not happy with the result but I'm happy with a big part of the game," he said.
"A lot of times when good teams play each other, the games are kind of boring, but this game was the opposite. And that was due to the desire, the passion, the greed of my team.
Klopp had the consolation of seeing Brazilian star Philippe Coutinho return, as a substitute for the final 15 minutes, for his first action since his potential summer move to Barcelona collapsed.
"Philippe trained the last few days really, really well," said Klopp. 2Maybe tonight in one or two situations he was not lucky but that was him without rhythm.
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