Liverpool's 3-2 defeat meant they were unable to take advantage of Manchester City's home loss to Manchester United and move to within four points of Manuel Pellegrini's side who lie fourth having played a game more.
But Klopp insists that with nine games remaining, his side can still challenge although he conceded they cannot afford a repeat of their second half performance at St Mary’s Stadium.
“There are 27 points still to play for,” said the Liverpool manager. “We can get all of them, there’s a chance. We don’t have to dream of things like this we have to play football and win games.
“If we played like the first half we can win games. If we play like we did in the second half it will be more difficult.”
Klopp was left stunned after his side had looked in control of the game at half-time after goals from Philippe Coutinho and Daniel Sturridge.
Southampton recovered to take the points with Sadio Mane scoring twice, the second the 86th-minute winning goal two minutes after Graziano Pelle had equalised.
“I’m not that good a loser so I don’t feel brilliant at this moment but this is football,” said Klopp.
“I know it’s like this. We have a few problems in the second half. We could have done better.
“I’m not angry, I’m frustrated of course because we got nothing. We played well in the first half and not in the second half so for me that sounds like a draw but we got nothing.”
Southampton manager Ronald Koeman greeted the winning goal with a dash down the touchline to join his players’ celebrations.
The manager, who was due to celebrate his 53rd birthday 24 hours later, admitted his reaction summed up the importance of this win to his side’s hopes of regaining a place in the Europa League next season.
“It is the first time I have done that and I think the last time. I am still tired,” he said.
“That happened because it was a must-win game for us today and when you are really down after half time you need to do everything to put the players’ hat on and go on and believe in yourself.
“You need to score the first goal to really get the feeling you can come back and get the result and that’s what makes it special and emotional. And of course all the goals were fantastic goals.
“I’m proud of the team. We had a great spirit after half time and it was hard to imagine it after 45 minutes. It’s my birthday tomorrow and this is the best possible present.”
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