The Reds defeated their arch rivals 2-0 at Anfield last week before grabbing a 1-1 draw at Old Trafford on Thursday night to progress to the quarter-finals 3-1 on aggregate.
United great Scholes, who has been critical of Louis van Gaal's side all season, says the Red Devils improved in the return bout but were still not match for Jurgen Klopp's Merseyside outfit.
"Over the two legs, Liverpool were by the far better team," Scholes told BT Sport.
"United were a lot better tonight - they had to be a lot better. They couldn't be any worse than they were last week.
"They huffed and puffed and they lacked the quality to score goals tonight.
"I always thought Liverpool were going to score goals and I was proven right."
Anthony Martial edged United back into the contest with a well-taken penalty in the 32nd minute before a delightful clipped goal from Philippe Coutinho on the stroke of half-time put the Reds back in pole position.