The Reds dominated the opening 45 minutes in Tuesday's third-round tie at the King Power Stadium but were unable to find a breakthrough.
Klopp told Sky Sports News after the game: "It's actually easy to explain [the defeat] - we played good football in the first half and missed big chances.
"That's football – it's at least 90 minutes. The goals we conceded are a second ball from a corner and a throw in again. I'm sick of [conceding] goals like this to be honest, you cannot play football and do that.
"The Leicester team somehow survive in the game as we aren't clinical enough. That is okay but then you need to stay concentrated. They scored too easy. With the first goal we don't push up together... I've said it 1,000 times."
Liverpool face Leicester again in the Premier League on Saturday.