Stoke were 2-0 down at half-time courtesy of goals from Graziano Pelle and Shane Long, but Steven Nzonzi halved the deficit before Mame Biram Diouf levelled matters with eight minutes remaining.
But moments after substitute Peter Crouch was sent-off, Pelle scored from the subsequent free-kick to send Southampton through to the last eight.
After his side fought back from a two-goal deficit, Hughes was disappointed it ultimately counted for nothing.
“We put in a huge effort in the second half,” he said. “We needed to because in the first half we didn’t really get anywhere near the intensity that I was hoping for in terms of making it a real cup tie.
“The difference with the second half was marked. It was a real effort and I thought the momentum was with us.
“At 2-2 I felt we were in the ascendancy and we could go on and possibly win it from a situation where at 2-0 down you think it’s going to be very hard against a very good Southampton team.”
Ronald Koeman argued Charlie Adam could have been sent off at 2-1 for a challenge on Morgan Schneiderlin that earned him a booking – one of seven shown by referee Lee Mason.
Hughes felt Crouch was a little unfortunate to see two of those – with the first coming for a clash with Jose Fonte and the second the late challenge on Davis.
“I felt the first yellow card was a little bit harsh on Peter,” said Hughes.
“I think he made a genuine attempt to just try to get across the lad. Whether or not the referee thought he raised his arm, I don’t know.
“The second one, he’s miscontrolled it and in trying to retrieve the ball he’s high. When you’re on a yellow card, there’s always a risk you’re going to get another one if you go in with a challenge like that.
“We’ve lost him, and that took a bit of the wind out of our sails, and then we haven’t dealt with a ball into our box.”