The Champions lost 1-0 at St Mary’s Stadium on Monday, and former player Danny Injaz scored a goal within two minutes before the Saints controlled Liverpool relatively comfortably.
Klopp saw Jorginho Wijnaldum’s shot from inside the penalty area, which was blocked by Jack Stevens’s hand before Kyle Walker Peters escaped punishment after Sadio Mane was dropped in the penalty area.
“The best situation we went through was when Sadio was holding the ball at his feet,” Klopp told Sky Sports. “For anyone to say they are a diver is the biggest joke … They have had two cases where the other teams get a penalty.
“Handball, I don’t know who will explain that to me. In these situations we were unfortunate.
“I heard that Manchester United got more penalties in two years than it was in five and a half years. I have no idea if it was my fault, or how that might have happened.
“But this is not an excuse for performance. We cannot change it, we have to respect decisions. We can change our performance. This is our focus now.”
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Liverpool have won five penalties this season, and have scored all five goals, with United being awarded six penalties and losing one. Leicester got 10, and scored eight.