United revitalised their season and blew open the Premier League title race by sinking leaders Chelsea 2-0 on Sunday in a tactical masterclass by manager Jose Mourinho.
Despite dominating last week's first leg against Anderlecht, United returned from Brussels with a 1-1 draw, but Young says they have no doubts about their ability to finish the job.
"We have felt that kind of performance coming," said the versatile England international, United's captain against Chelsea.
"There have been a lot of draws at home. I don't think a lot of people saw that scoreline coming or the type of game, to be honest. We did.
"We have belief in ourselves. I have confidence in every single player in the squad.
"Hopefully we have a semi-final coming up. If we can play like we did against Chelsea, then I am sure we can get through against Anderlecht and into the semi-finals."
United's win over Chelsea enhanced their chances of securing a top-four finish in the league, leaving them four points behind fourth-place Manchester City with a game in hand.
But whereas the path to a Champions League berth via the league remains steep, should they overcome Anderlecht, United will be just three games from securing qualification by winning the Europa League.
United are bidding to become only the fifth club -- after Juventus, Ajax, Bayern Munich and Chelsea -- to have won all three of Europe's major cup competitions.
They lifted the European Cup in 1968, 1999 and 2008 and the now defunct European Cup Winners' Cup in 1991, but have never previously gone beyond the last eight in the Europa League (formerly the UEFA Cup).
United are unbeaten in 16 European home games and have won all three of their previous home games against Anderlecht, including a club-record 10-0 rout in September 1956.
- Lyon shaken -
Mkhitaryan's 37th-minute strike at Constant Vanden Stock Stadium last week looked set to give United victory, only for Leander Dendoncker's header to draw Anderlecht level four minutes from time.
While Anderlecht's Swiss coach Rene Weiler acknowledged United's general superiority, he said Dendoncker's goal would give them belief for the trip to Old Trafford.
"It was difficult for us in the first half. Manchester United were really strong and very impressive," he said.
"We played better in the second half and higher up the pitch. We kept pushing because we knew we could equalise. That goal gives us extra motivation."
Lyon are braced for fresh turbulence as they take a 2-1 lead into the away leg of their tie against Turkish giants Besiktas at Istanbul's intimidating Vodafone Arena.
Last week's first leg was delayed by 45 minutes after fans clashed at Parc OL and Lyon's league game at Bastia last weekend was called off following a shocking attack on their players by rival supporters.
Speaking before the incidents in Bastia, Lyon president Jean-Michel Aulas expressed serious reservations about the return leg against Besiktas.
"I don't know whether the game should be played behind closed doors or somewhere else, but it would be very dangerous for us to play with the same supporters (as in the first leg)," he said.
"We're not very reassured about how things are going to go."
Peter Bosz's exciting young Ajax team carry a 2-0 lead into the second leg of their tie at Schalke, while Celta Vigo are 3-2 up prior to their game at Genk.
Fixtures (aggregate scores in brackets)
Thursday (1905 GMT):
Genk (BEL) v Celta Vigo (ESP) (2-3)
Besiktas (TUR) v Lyon (FRA) (1-2)
Schalke (GER) v Ajax (NED) (0-2)
Manchester United (ENG) v Anderlecht (BEL) (1-1)