Jesse Lingard's first United brace secured a routine 2-0 win as the competition holders made safe progress into the quarter-finals.
"But I don't think [it was easy] I think they have a good squad, a squad with lots of options".
Crystal Palace gained no respite from their Premier League struggles as they were beaten 4-1 away to Bristol City.
Mourinho made seven changes for this tie, with only Lingard, Chris Smalling, Ander Herrera and Anthony Martial remaining from the side shocked on Saturday.
Phil Jones limped off early during United's defeat in Saturday, while Eric Bailly remains sidelined along with Paul Pogba and Marouane Fellaini.
On the hour-mark, United scored again, with Lingard heading in after a superb team move.
Swansea celebrate pulling one back at home to manager-less LeicesterWhat time is kick-off?
But they were spared falling further behind when Scott McTominay lifted his shot over from the edge of the box.
Since the first minute we felt we were in the game.
Lingard then doubled his tally and the visitors' lead on 59 minutes with an exceptional header after a ball in from Matteo Darmian found him arriving at pace 16 yards out to header powerfully past Kristoffer Nordfeldt.
United should have had a third when Nordfeldt could only palm down McTominay's header and Tuanzebe blazed over from close range.
If the Portuguese needs to try to change the game at the Liberty Stadium, he can look to his bench and call for the experience of Nemanja Matic or the goals or Romelu Lukaku.