Both sides started fiercely, but it was Chelsea who started the quicker of the two, with Willian scoring in the 13th minute. Willian's goal will largely, however, be remembered as an Adrian howler, who fumbled the well-hit shot into his net.
Adrian had been forced into making several very good saves in the minutes leading up to the goal, but didn't do himself any favours over the goal.
The beginning of the second half saw Liverpool take control of the game, with an equaliser looking likely.
But it was the former Everton midfielder, Ross Barkley who had the final say in the game. His powerful solo run resulted in a goal in the 64th minute.
Klopp: I can explain Chelsea defeat
"Losing 2-0 is not good but in this case is relatively easy to explain," Klopp said.
"We made two massive mistakes around the goal. Adrian made a super save a few seconds before and then it's a really good shot from Willian but we lost the ball before that.
"We never thought it would be an easy game tonight. It was always difficult. We didn't do good enough in decisive moments and we have to accept that."
Klopp: our defence has got worse
Klopp conceded that his side's defensive ability to has declined over the course of the season.
"It went our way for so long because we defended outstanding," Klopp said.
"You didn't [used to] get a lot of chances against us. But now we are conceding too many goals, that's true. I'm not worried about momentum. You have to get it to keep it, we always have a chance to get it back.
"The performance was not bad. It wasn't like Watford. Tonight was a super intense game. A lot of sprints, a lot of spaces in midfield. You need accelerations constantly. That performance tonight, I'm not concerned about. But we made mistakes."
Though Klopp wasn't concerned about the FA Cup defeat, his side have now lost consecutive games and failed to score in both. In three of the last four matches, they haven't scored.
"The numbers are not cool," Klopp admitted.
"But the difference isn't 100 miles away. It's little things, but they make a difference."