United lost 5-4 on spot kicks after drawing 1-1 with Nigel Adkins' Hull City at Bramall Lane, after Billy Sharp's stunning volley cancelled out Jon Toral's first-half opener.
But United had what Wilder claimed was a legitimate goal ruled out when Enda Stevens was adjudged to be offside as he netted in the second half, and the United boss insisted: "The best team lost.
"We were excellent and they were hanging on at the end, wanting the referee to blow his whistle.
"I was delighted with the second-half performance and the first half was good, too, but it was disappointing to concede from a counter attack. Although they do have some quality players at the top of the pitch."
Wilder also praised referee Martin Coy for what he called an "unbelievable" decision to not award Jackson Irvine a penalty, after he appeared to be upended by Ryan Leonard in the United box.
"It looked to all the ground and where we were that it was a penalty, but when you slow it right down it's a fresh air shot from their lad and an unbelievable decision from the referee."