Marko Arnautovic's first-half effort was enough to secure a 1-0 victory after 90 minutes, but after an additional 30 minutes of action and a penalty shootout, it was the hosts who secured their passage through to the Wembley Final.
The Potters managed to defy the odds and turn the game back in their favour with a superb showing on Merseyside, but Joe Allen's penalty secured the Reds a 6-5 triumph and denied Hughes' troops a showpiece occasion in North London next month.
"I think the reaction of us all is pure disappointment because on the night we were by far the better team," Hughes told Stoke City Player following the clash.
"We came here, under difficult circumstances whereby we had to win the game, and won it.
"Obviously once it goes to penalties it can go either way and heartbreakingly for us it has gone their way.
"You can see by the reaction of their fans and their players that they have been incredibly fortunate to progress to the final.
"These sort of things happen in sport and football unfortunately, but that still doesn't make it any easier to take."
Despite the heart-breaking outcome, Hughes was full of credit for his troops, who he said executed his pre-match game-plan down to a tee.
"We had a plan, and as always you have to commit to it, and the guys went out there and made it happen.
"I can tell them what to do all day long but they have to go out there and actually put that into practise.
"I made a few changes which I think helped us. It allowed us to really dominate proceedings and create better opportunities than them in open play.
"It would have been fair if we were in a Wembley final, but that isn't meant to be - not in this competition anyway."
The City boss also acknowledged that he would be putting his arm around the shoulders of both Peter Crouch and Marc Muniesa, who saw their spot kicks saved by Simon Mignolet.
"What can I say to them? It is incredibly difficult, but both of those players were absolutely superb on the night.
"I was a striker, and paid to score goals and yet I never stuck my hand up to take a penalty in a shootout.
"It takes a lot of bottle to stand up and take one - especially in a game of such magnitude at a venue like this.
"I am full of admiration for them. It is just a shame their performances weren't rewarded with the outcome that they, and the rest of my players, deserved."