Just like in their last two outings, Klopp’s team needed late goals from Mohamed Salah and Jordan Henderson to move two points clear of City, who still have a game in hand.
“The performance was not top level but it is about fighting. People want us to play like Manchester City, we are unable to do that, we play our own football,” said Klopp.
“We have 82 points now, that is massive in this crazy league and everyone is waiting for us. I am really proud. It is incredible.”
Liverpool had to come from behind at St. Mary’s after Shane Long’s ninth-minute opener, but they levelled before half-time thanks to Naby Keita’s first goal for the club.
The visitors then dominated the second-half but had to wait until 10 minutes from time to go in front when Salah ran from inside his own half on the counter-attack from a Southampton corner to score his first goal for nine games.
Henderson started on the bench, but the Liverpool captain made a big impact with his first goal of the season to seal a vital three points.
“It is nice for Naby Keita to score the first to show Southampton it will not be easy for them. After that we controlled it more. It was good, I liked it,” added Klopp.
“It is a difficult year for everybody. You need to have 70-75 points for the Champions League and 90-something for the the title. We are in the race and that is nice.”
Liverpool appear to have the easier run-in from their five remaining fixtures compared to City’s six, that includes a visit of Tottenham and trip to Manchester United.
But Henderson believes his side will need to win every game to end a 29-year wait to win the title.
“It was very big. Every game is massive. We’ve got to win every game,” said the England midfielder.
“It was a big performance in the second-half and a big result.”