The Spanish side rescued a point at Anfield thanks to a curling effort from Joaquin Correa to see the match finish 2-2.
It was a fiery affair, with Sevilla boss Eduardo Berizzo being sent to the stands for throwing the ball away to waste time and Joe Gomez receiving a second yellow card in injury time.
Following the clash, BT Sport camera filmed Klopp confronting the opposition bench.
“Why are you shouting at me? Don’t touch me,” he yells.