The Reds lost 1-0 at the Wanda Metropolitano and were banking on home comfort to qualify for the last eight.
However, Klopp’s men could only score once in 90 minutes, taking the tie to extra time.
Robert Firmino made it 2-0, but Marcos Llorente struck twice to give Atletico a solid advantage at Anfield.
Alvaro Morata then sealed a famous win for Diego Simeone’s men.
“I don’t understand with the quality they have the football they play.
“They could play proper football but they stand deep and have counter-attacks.
“We accept it of course but it doesn’t feel right tonight. I realise I am a really bad loser, especially when the boys put such an effort in against world class players on the other side who defend with two rows of four,” Klopp told BT Sport.
