Two goals from substitute Wissam Ben Yedder within six minutes of his introduction set up a 2-1 victory in the second leg and on aggregate for the Spanish side.
Jose Mourinho told a post-match news conference he felt it was not a "bad" performance from United , but the club's former defender Ferdinand disagreed.
"They were terrible," Ferdinand said on BT Sport . "I didn't see this result coming, especially after the game against Liverpool [United winning 2-1 in the Premier League on Saturday], the way they played.
"They looked like a team thrown together, full of strangers. They played nervous and cautious from the beginning. In these games, you've got to go and take the game by the scruff of the neck. That takes personality, takes character in this stadium.
"You have to give the fans something to shout about. This stadium was quiet and that's down to the players on the pitch."
While few players other than goalscorer Romelu Lukaku emerged with credit from a humbling night for United, it was fellow forward Alexis Sanchez who Ferdinand picked out for criticism.
"Sanchez looks a shadow of the player he was," Ferdinand added. "At Arsenal he was the player everyone looked to for inspiration. Here he looks like a stranger in this team.
"When you go to a [new] team and play, you don't lose all your talent. That's what it seems like at the moment. In some ways I feel sorry for him.
"You could name him and the whole XI. The whole XI today were shocking."
Ferdinand's former United team-mate Paul Scholes indicated further investment in an already expensively-assembled squad will not be the answer for Mourinho's men.
"They keep spending money, keep spending loads of money, and we keep saying they're three or four players away," Scholes said.
"At some point, have they got too much money that they're throwing it away?"
@ManUtd forward line should be scary to play against....the team ain’t set up at times to get the best out of them. Lukaku often isolated, wide men defending deep, team sits deep....in glimpses they scare— Rio Ferdinand (@rioferdy5) March 13, 2018
Ferdinand later added on Twitter: "If you don't turn up with the right attitude and don't apply yourself then you will get beat - don't care what you have done or how good you have been before.
"The way Manchester United set up at Old Trafford today to counter attack this Sevilla team [weakest Sevilla team for years btw] was baffling.
"But also the players are the ones who set the tempo too, far too slow and cautious in possession and so passive without it."