With the two sides facing each other for the first time in European competition, Daniel Sturridge put Liverpool ahead from the penalty spot in the 20th minute after Memphis Depay brought down Nathaniel Clyne.
United failed to click into gear and Roberto Firmino made it 2-0 when he finished from close range after Michael Carrick failed to clear his lines in the 73rd minute.
The result gives Liverpool a comfortable lead heading into next week’s return leg at Old Trafford on Thursday night.
And former United midfielder Scholes was less than impressed by what he saw from Louis van Gaal’s men on Merseyside.
Speaking on BT Sport after the final whistle, Scholes said: “United were a shambles.
“At 2-0, they’re still in the game, don’t get me wrong.
“But when you’re at Man United I think there are certain standards you have to live up to and I think they’ve fallen well short.
“When we were coming through as players we had great examples likes Robson, Keane, Ince, Bruce setting standards – and we had to live up to those standards.”
He added: “I thought the biggest difference tonight was that Liverpool had a way of playing. United, I didn’t have a clue what they were trying to do.”
United now turn their attentions towards their FA Cup quarter-final clash with West Ham on Sunday afternoon.
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