Milner made a late appearance in the clash, replacing Alex Oxlade-Chamberlain with less than 10 minutes of regulation time remaining as Liverpool searched for the all-important winning goal.
Liverpool’s well-rounded performance, however, came unstuck as an Adrian mistake saw the dam wall break as Marcos Llorente netted a double and Alvaro Morata added the finishing touches, ensuring the title defence came to an end in the round of 16.
After an impressive display from Jurgen Klopp’s men, the result was a bitter pill to swallow as away goals proved decisive.
“They got their first goal and it took the stuffing out of us and, obviously, chasing the game at that point and [we] needed a goal – and then they got their goals on the breakaway.
“I thought it was a great performance from the start, we created a lot of chances against a very tough team who defend very well.
“The amount of chances we created we probably should have taken a few more of them.
“At 2-0 we’ve done a good job and at that point, obviously, just one goal changes it and that’s the cost of not getting an away goal.”
The Reds had a total of 34 shots on goal at Anfield, 11 of which were on target and two which struck the woodwork against a side who restricted them to zero on target in the first leg.
Klopp’s eagerness for unpredictability opened up a pragmatic Atletico defence and if not for the performance of Jan Oblak and some wayward finishing, Liverpool would have been home and dry.
But now, it is time for a swift response as the Reds look to finish the remainder of the Premier League season on a high.
“[They’re] very difficult [to break down],” Milner added. “They prove it week in and week out and it shows how good of a performance we [had] to create the amount of chances we did and the tempo the boys played at.
“Unfortunately, we just didn’t take enough of those chances and it’s massively disappointing but we have to pick ourselves back up and finish the season strongly.
“It’s disappointing. We wanted to go through, it was always going to be tough but we put in a great performance, the fans were fantastic.
“Away goals change games in European ties and that’s what happened, in terms of the rest of the season we have to pick ourselves back up and finish the season as strong as we can.
“That’s what we want to do and we want to win as many games as possible.”