Lingard was in good form Tuesday night as his goals helped United to a win.
Mourinho said: "We were in the game from the first minutes, pressing and forcing things, the attitude was good".
Shaw's route back into the first-team looked hard before United's win at Swansea but, with Tuanzebe impressing, he's even further behind now.
Swansea continued to push for an equaliser as half time approached and Sam Clucas nearly squeezed a curling shot into the bottom corner but the ball trickled just wide of the post.
The youngster's instead spent most of his time with the club's U23s and impressed coaches when he's trained with the first-team at United's Carrington training ground. United had to be satisfied with the two goals and a place in the next round of the competition.
According to the Manchester Evening News, Jones was flown with the squad and his inclusion for the trip to face Swansea will come as a welcome boost for United's next league tie against Tottenham Hotspur at Old Trafford. Tammy Abraham began warming up as soon as the second half started and most of stadium, along with this correspondent, hoped the striker would make an appearance sooner rather than later.
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It was a sensational finish and the goal not only doubled United's lead but also doubled Lingard's tally for the game.
Tuanzebe strode out of defence purposefully and spread a pass to Matteo Darmian on the right flank. Matteo Darmian produced the flawless cross, and the England worldwide was clinical at the vital moment.
With Spurs on the horizon at the weekend, Jose Mourinho is expected to try to freshen up his side, with key players like David de Gea, Nemanja Matic, Antonio Valencia and Romelu Lukaku expected to be rested.
Crystal Palace gained no respite from their Premier League struggles as they were beaten 4-1 away to Bristol City.
It ended up being a relatively simple victory for Manchester United but they once again looked laboured and sluggish in much of their attacking play.