The Red Devils edged Liverpool 1-0 in the third round of the Capital One Cup in a hard-fought contest at Old Trafford which was warmly welcomed by Smalling.
"It was a massive turnaround," he told Sky Sports 1.
"It was a big stage for us to go out there.
"There was a lot of doubt at the weekend, we needed to go out and put on a performance."
He added: "I felt like it was end to end for pretty much 90 minutes.
"It shows we can go out there on the big occasion and produce."