The Potters held the reigning Premier League champions for 62 minutes on Wednesday, before their resistance was broken and they ended up on the wrong end of a 2-0 scoreline.
United now march on to the semi-finals, while Stoke are left to turn their attention back to the pursuit of points.
Hughes believes there are positives to be taken into the busy festive period, with his side proving again that they are a match for the best in the business on their day.
The conditions on a windswept night at the Britannia Stadium - which saw the game halted for 10 minutes during the first half - helped neither side, but it was United who ultimately offered enough to get over the line.
Hughes told Sky Sports: "We made a fair fist of it in the first half, against all the elements. We stuck at it and I thought we were in decent shape.
"I thought our organisation was good and United weren't creating too many problems for us and we had a couple of chances where we got balls into the box.
"Obviously we came out second half thinking the elements would be with us, but they disappeared so we didn't get the advantage of that. That's not to say that United, on the night, didn't deserve to win."