The visitors made light of having to play twice in three days as Jermain Defoe and Paulinho struck either side of half-time before Nacer Chadli blasted in and Defoe tucked home his sixth of the season to give them a deserved win.
And after the match, the Portuguese manager was grateful to his strength in depth as the north Londoners outclassed their Premier League opponents at Villa Park.
"It was a great performance and a great response from the team," he told Sky Sports.
"We came here with three players who played that game (against Cardiff on Sunday), so it was a risk, but we have great strength in depth.
"We have great team spirit this year and all the players are buzzing for opportunities like this so I think most of them really, really performed out there.
"We have that strength in depth to be playing after just two days, so we use it.
"What is so good about this evening is that the players responded in the right spirit and a great sense of responsibility towards the competition and did extremely well."
Meanwhile, Villa boss Paul Lambert felt the eventual scoreline was harsh on his team.
And the game hinged on a bizarre incident at the start of the second-half when substitute Nicklas Helenius got round the back of Jan Vertonghen as they chased Matt Lowton's forward pass into the box.
In his desperation to recover the lost ground, Vertonghen stumbled and as he was falling made a grab for Helenius. The Belgian succeeded only in grabbing the striker's shorts, yanking them down to his knees just as he was about to shoot.
Helenius carried on anyway, blasting over from an acute angle.
To Lambert's disbelief, referee Jon Moss opted to give a goal-kick rather than a penalty that surely would have been accompanied by Vertonghen's exit.
"It is the first time I have seen something like that happen," said the Villa chief.
"You hope you get those decisions. I don't think anybody could believe he wasn't pulled back."
Lambert wondered whether Villa would have got the spot-kick had Helenius opted to go down rather than stay on his feet and go for goal, although he did recall a similar incident at Arsenal on the opening day of the season.
"I thought that myself," he said.
"But does it matter whether he has shot or not? At Arsenal the referee waited.
"I have certainly not seen anything like that before."