The Reds boss also appeared to take a dig at rivals Manchester United, who have been awarded several controversial penalties this season, as his team were overlooked spot kicks of three occasions on the south coast.
Two of those involved former Saints player Sadio Mane, who twice went to ground in the box, and Klopp was particularly unhappy those were overlooked.
“If anyone ever said that Sadio Mane is a diver, it’s the biggest joke in the world,” he told Sky Sports. “This boy tries to stay on his feet. I think there were two situations. Other teams would get a penalty for that, put it that way.
“And then there was the handball. Someone’s going to have to explain that to me.
“Let’s not take anything away from Southampton, but in these situations we were unfortunate at least.”
Klopp did admit, however, that his side should have defended a second-minute free kick, which allowed Danny Ings to open the scoring, better.
“A slow start made life massively difficult for us tonight,” he said before lamenting Trent Alexander-Arnold’s part in the goal.
“We had a player there who was there to clear the ball but he missed it. Then after that, it’s a great finish. But we could have defended it.”
He also agreed that home goalkeeper Fraser Forster should have been more significantly extended.
“With the possession we had, he should have had much more to do,” he said, having watched his side muster just one shot on target.
“That’s the situation we put ourselves in. We wanted to start completely differently. We had a long, long spell in the second half when Southampton had nothing to do with the game. The best chances were when pretty much Mane had the ball.
“We're having a rather rusty moment. We're not blind. We have to fight through this and play through this, but there are proper opponents around. The attitude of Southampton tonight was exceptional.”
The sides are presently locked together at the summit of the standings, but should the Red Devils avoid defeat in a game in hand against Burnley, they will be at the summit by the rivals lock horns.