The Red Devils are into the last-16 alongside their fellow Premier League rivals after beating Real Sociedad in the round of 32.
Ole Gunnar Solskjaer's side are hoping to atone for last season's semi-final loss in the same competition, and Scholes thinks they can use the defeat as motivation in the upcoming rounds.
He told BT Sport: "It hurts him. Four semi-finals for him which isn't great because you need to go to that level now.
"You've seen them do well to get to second in the league, then fall away. They went top then unfortunately they went on a sticky run and fell away.
"They have got to find that extra quality, big players in big games. If Man Utd want to go to the next level, win titles, win cups - these players need to step up."
He added: "Man United can (win the Europa), not sure about the other (British) teams. Man Utd have the best squad in the competition. This is a great chance for United to win something.
"They (the other British clubs) think they are in a good chance, but Man United are much better than Arsenal and Tottenham. Italian football and Spanish football are nowhere near as good as it used to be."