The absence of Trent Alexander-Arnold due to illness meant Milner had to fill in at the fullback position.
The 35-year-old, who has played there on many occasions earlier in his career, barely put a foot wrong against Palace.
"He loves the position, whatever he says!' Klopp told reporters.
"Milly did an incredible job. I'm pretty sure he enjoyed that."
"Cheers, Trent!" added Milner, referencing his teammate missing the game.
"Zaha is one of the trickiest customers in the Premier League. He's strong, he's quick, he's unpredictable.
"There were moments when I wasn't as sharp as I can be. But that's why I'm here. If something is needed, try and do what you can."
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