The Reds are still top on goal difference, but Manchester United have a game in hand and could be top ahead of the champions by the time the teams meet at Anfield in Liverpool’s next league game.
While Klopp acknowledged Southampton were worthy victors on the night, he also felt an improved showing in the second half was a step in the right direction – largely thanks to Sadio Mane’s efforts which went unrewarded, despite appearing to be fouled in the box.
“It was a great finish [for the Danny Ings goal] but we could have defended it [better]. With the way we played Fraser Forster should have had much more to do, but that’s the situation we brought ourselves in,” Klopp told Sky Sports at full-time.
“We had a long spell in the second half where Southampton had nothing to do with the game, no counter-attacks, nothing. But the best situations were with Sadio. If anybody calls him a diver it’s the biggest joke in the world.
“This boy tries to stay on his feet with all he has. With two situations other teams would get penalties, let me say it like this. Then a handball…it doesn’t make our performance better and shall not take anything away from Southampton, but in these situations we were unfortunate at least.”
The defeat for the Reds follows draws with West Brom and Newcastle and Liverpool have now dropped more points this term than they did last year in winning the league.
Klopp said his team are in a tough run, but pointed out they will simply continue to work through it and eventually show their quality.
“I wish we only had the problem away from home. We drew at home against West Brom for example. It’s a rather rusty moment and we have to admit that, why should we not?
“To solve the problem you have to know the problem, we are not blind for our problems. We just have to fight through this and play through this. It’s up to us to change that.”