Liverpool were held to a score draw on their first Champions League group match since 2014.
After Saturday's 5-0 defeat to Manchester City, Liverpool were desperate to make amends.
But it was a terrible start from Klopp's side as Wissam Ben Yedder opened the scoring for the visitors after just five minutes.
Goals from Roberto Firmino and Mohamed Salah flipped the score-line, although the former missed a penalty just before half-time.
Liverpool were on top for the majority of the second half and missed several guilt-edge chances and were punished on 72 minutes when Joaquin Correa equalised with Joe Gomez being shown a second yellow card in stoppage time.
But things were getting heated on the touchline between Klopp and Eduardo Berizzo with the Sevilla coach throwing the ball away to stop Liverpool taking a throw.
The second time led to Berizzo being sent to the stands and, before being led down the tunnel by a policeman, he attempted to speak with Klopp who turned his back on the Sevilla boss.
And feelings were clearly still heated after the game when Klopp went to shake hands with the Sevilla bench.
The Liverpool manager could be seen looking flustered as he asked: "What have I done? Why are you shouting?
"I didn't send him off!"
And in his post-match interview on BT Sport Klopp tried to explain it wasn't him who got the Sevilla boss sent off.
"Can I like the situation? Probably not but I don't think I had any influence on the decision from the referee," Klopp said.
"I didn't ask for it or whatever.
"We had a talk between ourselves and we were fine.
"But people on the bench thought I'm responsible for this red card so they didn't like me too much but it's not a problem."
In the midst of all the drama, Philippe Coutinho made his return to the Liverpool side as he came on in the second half for Emre Can but was unable to make an impact on proceedings.
Daniel Sturridge also made his Champions League debut for Liverpool despite being at the club since January 2013, coming on for the final six minutes.
But on a night where there was much anticipation about Liverpool's return to Europe's elite club competition, it ended with the same murmurs of discontent that has cost them dearly in recent years.
A potentially tricky away trip to Spartak Moscow awaits Liverpool in the next round of the tournament in two weeks time.
But their attention will swiftly turn to Saturday's visit of Burnley who have already caused one upset this season after beating Chelsea 3-2 on the opening day of the season.
Source: Daily Express