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For the second season running, the Reds were knocked out of the European competition by a Madrid side after a 3-1 aggregate loss.
The damage was all done in the first leg at the Alfredo Di Stefano Stadium courtesy of a Vinicius Jr brace and Jurgen Klopp's side were unable to overturn the deficit in the second leg, which finished 0-0 at Anfield last night.
Liverpool were guilty of spurning a number of big chances and Milner, skipper on the night in the absence of Jordan Henderson, rued those misses.
`"The positive is that we are creating them, especially against a team like Real Madrid, and the reaction we showed from the first leg," Milner told BT Sport.
"We did enough tonight to go through, I believe that with the chances that we had.
"We were obviously the better team. He [Courtois] made a good save, but if you don't take your chances you're not going to go through.
"You only need that first one, if you get the first one in then it changes the game."
The Premier League champions will end this season trophyless but Milner says the team are desperate to be playing in Europe's premier competition next term by securing a top four spot.
With seven games remaining, the six-time European champions are currently in sixth place, three points off fourth-placed West Ham.
Milner added: "If we perform with that intensity and desire and tempo that we played with tonight for the last [seven] league games then hopefully we can get into those top four spots.
"But that's the most important thing, that we replicate this form and these sort of performances. That's the one thing we've been missing, that consistency we haven't had.
"So that's what we need to get back, have a big push these last few games and put this disappointment aside."
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