The fifth-placed Reds arrived at St Mary’s knowing they had already missed out on a top-four finish for the first time since 2015-16.
But they were forced to come from 4-2 behind to stretch their unbeaten run to 11 games following Kamaldeen Sulemana’s brace and strikes from James Ward-Prowse and Adam Armstrong.
Liverpool boss Klopp, whose side avoided defeat thanks to a goal from substitute Cody Gakpo and Jota’s second, was happy to see the back of 2022-23 and confident next term would be far more memorable.
“There were moments during the season when you thought ‘the season will be four years long’,” he said.
“Thank God for the last 11 games, that helped massively, gave us a real boost, gave us a perspective, gave us a basis for what we have to do.
“That it didn’t turn into the best ever season, we see that, we know that, we are very disappointed about the fact that we didn’t make it to the top four.
“But there are moments when you have to admit there were four teams that were better than us – that’s the truth.
“We played a bad season, we come fifth, that is a message as well.
“Imagine we were our normal self, which we absolutely will be again next season and will be a contender again. That’s how is it. The last 11 games helped us to realise that again.”
Gakpo and Jota struck in the 72nd and 73rd minutes respectively to prevent Liverpool slipping to a shock defeat, while Mohamed Salah hit a post late on.
Klopp felt his players contributed to their own undoing during a “silly” period of a chaotic contest.
“We are 2-0 up and you know these Southampton players want to pay back to these [home fans] and we let them, just opened the door for a really talented offensive team, with the speed they have,” he said.
“I can make a list of things we weren’t and that led to the counter attacks they had.
“Then it’s 2-2 and 4-2 and then we started doing the right things again. I think we could have scored a fifth and a sixth.
“Top start, outstanding finish, in between just silly.”