Liverpool enjoyed most of the possession at St Mary’s, but their first shot on target only came in the 75th minute as they failed to score for a second successive game.
The reigning champions remain top of the table on goal difference from Manchester United, but Klopp knows his players need to quickly find their form.
“I know they are great guys, super boys, fantastic football players, but tonight they were not good,” the Reds boss said.
“If I think they should have done better then I get angry, not for long, but I get angry. They know that. It was always like this.
“Just because they won something in the past, doesn’t mean you are always like this.
“We don’t have to make it bigger than it is, but we didn’t win the last three games. That’s all our fault, mainly my fault, but the boys had a hand as well and we have to change that.
“If you bring yourself [into] a situation like you did tonight, against an opponent like Southampton, then you play with fire.
“No, you do that because you put them under so much pressure that they cannot cope any more. Southampton were on the edge of that, but we helped them. That’s all. We were not good enough tonight.”
Southampton’s victory moved them into the top six, just four points behind the leaders.
Ralph Hasenhuttl’s side have lost only two of their last 15 Premier League games – home defeats to Manchester United and Manchester City – and he was delighted his players had managed to beat one of the big teams.
“We had an unbelievable mentality, maybe more than they had,” the Saints manager said.
“But I think we never gave up and tried until the end to turn things around but I think we showed that it is possible to win against such teams and we did it against the best team.
“It’s fantastic. The good thing is you don’t expect to take points against this team so I think this was bonus points that you take and especially a win for the belief and for the guys because they are happy.”