Liverpool went out of the Cup after a 2-1 loss at Brighton in the fourth round, having lost 3-0 at the same venue in the Premier League on January 14.
The defeat followed Liverpool's exit from the League Cup in the last 16 and underlined their poor form this season, with Klopp's team currently ninth in the Premier League at the halfway stage.
"We have still space for improvement. We make steps but we have to improve, we have to improve further and that's what we will do," Klopp told reporters.
"Look, I am not over the moon about this performance but, again, the only thing that happened really is that we lost against a good side, who we lost (to) two weeks ago in a horrendous game," he added.
"Today was much better. With the performance from today two weeks ago, that would've looked different as well."
Klopp said his team had closed the gaps for the greater part of the game but were guilty of conceding from set pieces as Brighton came from behind to beat the six-times European winners.
"It's not that we were that much under pressure, we had our moments as well in the late period of the game. That's how football is, everything opens up a little bit," Klopp said.
"Again, the goal happened after a set piece and the set piece shouldn't have happened because we could have won that ball in a heading situation already."
Liverpool next play away to Wolverhampton Wanderers on Saturday in the Premier League.
