Trailing 3-0 to Atalanta after the first leg at Anfield, Mohamed Salah's early penalty in the return match on Thursday gave Liverpool a 1-0 victory in Italy but Klopp's side went out 3-1 on aggregate.
"Disappointed that we did not go through but not frustrated or angry. Now we can focus on the league and that's what we will do," Klopp told reporters.
"We have a few days to recover and then we play Fulham, which will be tricky but we will give our absolute all. That's our competition now."
Third-placed Liverpool are level with Arsenal on 71 points but trail on goal difference. Leaders Manchester City have 73 points.
Klopp said he was not concerned about Salah's form when asked about the forward's performances in recent games.
"The penalty was super-convincing, a super penalty, then the next chance, that was obviously unlucky but it is not the first time he missed a chance like that," Klopp added.
"I am not particularly concerned. That's what strikers do, that's what happens to strikers, its how it is."
