Zlatan Ibrahimovic and Anthony Martial both struck twice as United eased to a 4-1 victory at Old Trafford on Wednesday.
Manager Mourinho stayed out of sight after accepting a one-match touchline ban earlier in the day for his sending-off during Sunday's Premier League draw against the same opponents.
The Portuguese was inside the stadium but was only seen before and after the game when, after previously bemoaning his side's luck, he expressed his satisfaction with the outcome.
"I'm pleased with the goals because the performance is something we're used to," Mourinho told Sky Sports. "Goals plus performance means the real happiness."
Asked where he watched the game, Mourinho said: "It's a secret."
United conceded after just 90 seconds on Sunday but this time roles where reversed as Ibrahimovic fired them ahead in the second minute.
The hosts should have added more but squandered numerous chances before United academy product Ashley Fletcher stunned them with a shock equaliser against the run of play after 35 minutes.
Manchester United transfer targets
Manchester United transfer targets
1/6 Jose Gimenez (Atletico Madrid)
The 21-year-old Uruguayan has already played 21 times for his country and has been touted as a future world-class centre-back. Currently on the books of Atletico Madrid, Gimenez is not a regular and a move in January for first-team football would surely appeal to him.
2/6 Victor Lindelof (Benfica)
The most recent player to be linked with the Red Devils, Lindelof is a 22-year-old centre-back currently plying his trade at Benfica. The Swedish international has been in fine form this season and could be tempted by a move to England in January.
3/6 Mesut Özil (Arsenal)
The German midfielder has emerged as a shock transfer target for the Red Devils as the Arsenal playmaker demands a substantial increase to his current £140,000 per week contract in North London.
4/6 Antoine Griezmann (Atletico Madrid)
The French forward had a brilliant season in Spain last year and was top scorer and Player of the Tournament as he helped his country to the final of Euro 2016. Atletico Madrid would certainly not let him go on the cheap however.
5/6 Yannick Carrasco (Atletico Madrid)
The third Atletico Madrid player reported to be on Mourinho’s wish-list, Carrasco is one of Belgium’s new generation of talent and, at just 23 years of age, has a long career ahead of him. The Belgian is an attacking midfielder who has added a ruthlessness in front of goal to his repertoire this season, contributing nine goals in all competitions.
6/6 Bruma (Galatasaray)
Galatasaray’s fleet-footed winger is rated at around £21.5m and has impressed in the Turkish league this season, receiving five Man of the Match awards in just ten starts so far. Bruma is a fantastic dribbler who would certainly provide competition for places on the left wing.
United hit back early in the second half with Martial's two goals - the Frenchman making a point after being left out at the weekend - securing victory. Ibrahimovic added gloss to the scoreline in stoppage time.
United will now play Hull for a place in the Wembley final.
Among the other positives for United were the excellence of Henrikh Mkhitaryan, continuing his recent rejuvenation, and the return from exile of Bastian Schweinsteiger with a late cameo off the bench.
Captain Wayne Rooney was also impressive but was ultimately frustrated in his quest to score the one goal needed to equal Sir Bobby Charlton's United record of 249. He will now have to wait at least another week for a chance to reach the landmark after a booking landed him with a suspension for Sunday's clash at his former club Everton.
West Ham boss Slaven Bilic admitted his side were outplayed.
He said: "I'm very disappointed, they deserved it. You can't expect anything here when you have such a slow start to the game."