United dominated the game and took the lead through Chris Smalling’s scuffed shot in the 37th minute.
Juan Mata made it 2-0 with an 18-yard free-kick on the stroke of half-time, before Jesse Lingard tucked in the third to add gloss to the scoreline in the 61st minute.
The victory will go some way towards easing the pressure on Louis van Gaal, who had watched his side lose back to back games heading into Monday’s clash.
And although Hoddle was impressed by United’s performance, he admitted that Shrewsbury did little to test their opponents.
Speaking on BT Sport after the game, Hoddle said: “They showed a lot of professionalism and kept the ball but it was made a bit easy by Shrewsbury, I’ve got to say.
“We thought it was going to be an awkward night for United but they made it comfortable by not pressing them and not getting at them.
“I think they’ll really regret the fact that they didn’t really give it a go.”
The win sets up a quarter-final showdown with West Ham United at Old Trafford.
United take on Arsenal in the Premier League on Sunday afternoon.
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