Harry Kane was back on the scoresheet for Spurs, with Son Heung-Min also scoring for the home side while Diogo Jota and Andy Robertson scored Liverpool’s goals.
Liverpool finished the game with ten men after Robertson was sent off in the second half but Klopp believes Kane should also have been dismissed for a first half challenge on the Scotland captain.
The Reds also had a penalty call involving Jota waved away by Tierney.
"I have really no idea what his problem is with me," said Klopp, who spoke to the referee at half-time and full-time.
"We can give Robbo a red card... that's not the smartest challenge of his life, that's how it is, but that's definitely a red card [for Kane], no doubt about that.
"People will say his leg was in the air, but that's pure coincidence. Harry cannot judge that and if Robbo's leg is on the ground then it's a broken leg.
"We have VAR sitting there and he looks again at the Robertson situation, fine, that's what he's there for. What did he do in that [Kane] situation?
"And the penalty situation with Diogo Jota, Mr Tierney told me he thinks Diogo stops on purpose because he wants the foul.
"First and foremost, if you want to shoot you have to stop because you cannot run and shoot in the same moment. It would always be helpful if you play football yourself in the past.
"When you see the situation back and the VAR's there, where is he stopping? You have two challenges against one player and the player's down. I don't understand that."
Liverpool are now three points behind leaders Manchester City.
