The Reds are 10 points behind leaders Manchester City having played two games more following Saturday’s 3-1 defeat.
Alisson’s mistake, when he raced out of his goal and collided with Ozan Kabak, allowed Jamie Vardy to put Leicester ahead with nine minutes left.
James Maddison’s free-kick had levelled just three minutes earlier after Mo Salah gave Liverpool a second-half lead.
Harvey Barnes made it 3-1 with five minutes remaining – lifting Leicester into second – and Klopp conceded the title.
“Yes. I don’t think we can close the gap,” he said after a third straight Premier League defeat.
“We have to win football games and big parts of the football were really good. We have to avoid mistakes and misunderstandings.
“Today we didn’t do that. The rest of the game was really good. First we have to perform again, results are massively related to the performance.
“We are not worrying about the title, we are not silly.
“With the majority of the game I agree it was a really good game. It’s not easy to dominate Leicester in the way we dominated.
“We scored a great goal but conceded a strange one and I think it’s offside and the 2-1 is a misunderstanding.
“That had too big an impact on the game. We had to show a different reaction and the third we gave away too easily.”
Liverpool were brighter for much of the game but Vardy missed two fine first-half chances when he headed at Alisson and hit the bar when Maddison’s flick sent him clear.
Trent Alexander-Arnold struck the bar with a 30-yard free kick after the break before Salah opened the scoring, curling in after 57 minutes from Roberto Firmino’s cute touch.
But Liverpool’s hopes of closing the gap on Manchester City came crashing down in the last 14 minutes.
First Leicester were awarded a penalty when Barnes was tripped by Thiago, only for VAR to rule it was outside the box.
Maddison, though, immediately curled the free-kick from the left into the bottom corner and the goal was given following a VAR check which adjudged Daniel Amartey was just onside.
Alisson then handed the Foxes the lead with nine minutes left when he came for Youri Tielemans’ pass but crashed into Kabak instead for Vardy to run the ball into an empty net.
Alisson turned a Vardy effort onto the post and Barnes then made it 3-1 after latching onto Wilfred Ndidi’s pass to lift the Foxes above Manchester United.
“This was going to be a good measure of the development of the team. Our reaction throughout the game was very good,” said boss Brendan Rodgers.
“It was a fantastic win against the champions, I thought we deserved it.
“They made a good start to the game. In the first half we were a bit more passive than I would have liked.
“If you are going to play against a top team you have to be aggressive with and without the ball. They are a top side, that’s why they are champions.
“Whatever happens the players have shown maturity and consistency. This group has got big potential and just needs time and consistency.
“Just missing out (on the top four) last year has helped and this year we are seeing them cope better.”
REUTERS