The defender played 90 minutes, helping United to a clean sheet on the way to a 1-0 victory, and believes that rediscovering winning form was the minimum requirement after Sunday's 4-1 loss to rivals Manchester City.
Smalling told Sky Sports: "It was a massive turnaround [from the weekend] and especially as there were a few players who have not played a lot of games. There was a lot of doubt after the weekend and we wanted to go out there and put on a performance.
"It was a big stage for us to go out there and the fans were really behind us – the noise they created was fantastic."
A second-half goal from Javier Hernandez settled the contest, sending United into the fourth round where Norwich City await, and Smalling believes the game was a good chance for the players to prove themselves to David Moyes.
"It felt like it was end-to-end for pretty much 90 minutes – there were a lot of chances created and it was a real cup tie. It was a chance for us to show him [Moyes] as he’s not seen too much of us, other than in training, to go out there on the big occasion and produce."
Look out for an exclusive interview with Chris Smalling in Saturday’s edition of United Review, the Reds’ official match programme.