Christian Benteke’s third goal of the season had given the hosts a 77th-minute lead, only for Sadio Mane to equalise at a set-piece four minutes from the end before getting sent off for a second yellow card in added time.
“They work so hard and are full of concentration and passion. Everything is there but we concede one goal and it felt like the end of the world. But it is not the end of the world, you can always come back,” said the German.
“I really don’t understand this pressure in this moment but the guys feel it and you can see it.
“The free-kick; everyone knows you should not concede things like this against a team like Southampton with their strength in the air and there were three one-on-ones in the air and it is a draw.
“We did not give up physically but we didn’t believe any more that we could turn this game and that is a problem.
“I wouldn’t say it is a negative mentality. First of all you have to recognise it is like it is, it is not a sickness and you can change everything.”
Klopp is still looking for his first win since taking over, but even after a third successive draw he believes they are making progress.
“There were many good moments in the game,” he said. “We can talk about why we didn’t make the next step but we all know it takes time and I see development.
“But the other teams don’t wait for us. They want to beat us and I am sure you don’t think it was an easy game for us.
“We have to understand that it is football, all of us. We don’t get help from outside because we have to deliver results all the time.
“We haven’t lost until now against not the worst teams in the league and that is okay, but it is not enough. “We have to accept this and work. I saw many things tonight I can work with.
“I saw things that were better, some that were not so good; some of these things were because we played on Thursday but it is like it is.”
Klopp celebrated Benteke’s goal like it was the winner and admits he may finds it difficult to keep his emotions in check, even when experience tells him he should.
“It was an absolutely fantastic goal,” he said. “I learned in my life you should celebrate a party when you have one as you don’t know when the next one is.
“It was a moment. Now I know – don’t celebrate too early. Hopefully we don’t have to wait too long (for the next one).”
Southampton boss Ronald Koeman accepted his side were below their best but felt they were worthy of a draw. “I think we deserved one point, if not more,” he said.
“One of our qualities is to keep the ball and have good attacking movements and create chances, and I think our offensive performance was not good enough because Liverpool played strongly physically and defensively.
“We can do better offensively than we did today. There wasn’t a lot of opportunities for both teams; it was a great goal for Benteke but a good reaction from our team.
“We can play better football than we can today.”
LIVERPOOL 1-1 SOUTHAMPTON
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