"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.
Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Atalanta have a chance to make history on Thursday as they welcome Liverpool to Bergamo with one foot in the Europa League semi-finals thanks to a stunning first-leg win at Anfield.
Jurgen Klopp was headed for a glorious send-off in his final season at Liverpool just a few weeks ago, but talk of a potential quadruple is now long forgotten as the Reds have come off the rails.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
AC Milan, Marseille, Roma and West Ham were among the other sides to also book their place in Friday's quarter-final draw.
"The present is more important. The past is the past. We don't know the future," Mourinho said.
AS Roma grabbed a 1-0 home victory over Bayer Leverkusen in their Europa League semi-final first leg on Thursday thanks to 20-year-old Edoardo Bove's second-half goal.
Federico Gatti scored with a header seven minutes into added time to earn Juventus a 1-1 home draw against Sevilla in their Europa League semi-final first leg on Thursday.
Liverpool will take the chance to qualify for the Europa League as they look to squeeze everything out of a disappointing season, manager Juergen Klopp said ahead of Sunday's home Premier League game against Tottenham Hotspur.
Manchester United have been hit by a double defensive injury blow after Lisandro Martinez was ruled out for the rest of the season and Raphael Varane sidelined for the next few weeks.
Marcus Rashford will miss Manchester United's Europa League quarter-final first-leg clash with Sevilla after suffering a muscle injury that is likely to keep him out for "a few games", the club announced on Wednesday.
"It was very important. This match was for you, Ukraine, it was for our country, for Ukraine," said Croatian national Jovicevic who has worked in Ukraine for more than 20 years
"I am happy with the performance, it was not an easy game after the first-leg result, as the crowd here is very passionate," Juve manager Massimiliano Allegri told Sky Sport Italia
Fernandes told BT Sport. "The belief of the fans, they push us through difficult moments. We have made great comebacks, the club is made also by that. In the past we have done a lot like this result"
"Above all, we need the bring the mentality to compete in Europe. We can say that Manchester United have returned and they are playing their best football in many years. It is a good opportunity to show that Barca can also compete," said Xavi