A goal from Sadio Mane, adding to the goals he scored against Chelsea en route to the Reds’ penalty shoot-out victory over Chelsea, and one from Roberto Firmino were enough to see off the Saints at St. Mary’s on Saturday as Liverpool kept up their 100 per cent start to the season.
A mistake from stand-in goalkeeper Adrian, whose heroics in Istanbul had helped clinch a first trophy of the season for Klopp’s side, allowed Southampton back into the match through Danny Ings in the closing minutes.
And Klopp, speaking to BBC Sport, said of his side's recovery from playing 120 minutes in Turkey on Wednesday: "It was so difficult for us today. We showed from the first second that nobody was tired today. We were here to win the game, that was the only reason, so we had to fight like crazy.
"I said before the game that most of the headlines were written, everyone was prepared for what looked like a banana skin, because Southampton had lost their first game and we had problems here last year.
"Our plan for the headline was 'the mentality giants are in town' - that was my headline. I thought the boys fought for each yard of the pitch and played good football and scored wonderful goals."
Liverpool had had less than three days to prepare for their trip to the south coast following their win in Turkey, arriving back in the UK just 36 hours ahead of kick-off at St. Mary’s.
“We had no time, we came back late on Thursday and the coaches sat in a meeting together to watch games of Southampton,” said Klopp. “Friday we showed the players and then came here.
"We had a proper sleep of course and then played the game, that's how it is."
Liverpool sit top of the early Premier League table after two games following on from their 4-1 win against Norwich on the season’s opening day.