Shinji Okazaki’s goal and a wonder-strike from Islam Slimani gave Leicester a 2-0 third-round win.
A frustrated Klopp, whose side have failed to win or keep a clean sheet in their last four games, told Sky Sports: ‘I am sick of goals like this. Leicester somehow survive in the game because we’re not clinical enough. They scored too easily.’
The game turned at half-time when Philippe Coutinho was withdrawn for Ben Woodburn and Liverpool lost their attacking spark.
He said: ‘After the first goal you saw the heads from Leicester went up, that was a bigger difference. The game changes in moments like this, you have the chance to do it by yourself or sometimes you are on the wrong side and that’s how it is.
‘But that we concede like this, that makes me really, really sick.
‘We are still a good football team, I see it, but unfortunately it doesn’t feel (like that) at the moment because it’s a cup competition. We wanted to go into the next round and nobody is interested who plays the better in the first half.
‘The story of this game is really easy to tell, we were the much better team in the first half, we played good football, we didn’t score, that’s sometimes part of football.
‘But as long as we concede goals like we conceded today, then it is quite difficult.’
Coutinho was replaced by Woodburn at half-time as he returns to fitness following a delayed start to the season, which saw Liverpool reject up to £114million from Barcelona for the midfielder.
And Klopp defended the decision to take the Brazilian off, despite him being Liverpool’s best outlet.
‘That was the plan before the game. He needs match time but it was not the plan to let him play again 60 or 70 or 80 minutes,’ said Klopp.
‘Forty-five is the limit. We need to get him fit but we cannot push him through.’
Coutinho, Alex Oxlade-Chamberlain and Dominic Solanke wasted fine openings in the first half before Okazaki and Slimani struck after the break.