The Potters bowed out on penalties after finishing 1-1 on aggregate in the two-leg semi-final, following their first win at Anfield since March 1959.
Stoke's goal in first-half injury time by forward Marko Arnautovic owed a lot to good fortune.
"It was offside, but we deserved it. We got the goal that won us the game, but not the tie," Hughes told BBC Stoke.
"We always thought we had a chance even if others didn't, but we just couldn't get that second goal even though we looked the likelier side to score.
"You can see by the reaction of their fans and their players that they have been incredibly fortunate to progress to the final.
"Obviously once it goes to penalties it can go either way and heartbreakingly for us it has gone their way. These sort of things happen in sport, but that still doesn't make it any easier to take."
Stoke, who lie ninth in the Premier League table, just a point behind Jurgen Klopp's seventh-placed Liverpool, were up against it after a disappointing performance in the first leg at the Britannia Stadium three weeks earlier.
However, despite being without skipper Ryan Shawcross at the back, with Marc Muniesa coming in, the Potters prevented Liverpool managing a single effort on target.
And a return to old Tony Pulis tactics with the selection of big men Jon Walters and Peter Crouch up front made them more of an attacking threat than the home side.
"To a man I can't fault any of them," said Hughes. "They all put in fantastic performances. I'd highlight Peter Crouch who, along with Marc Muniesa, hadn't played for a long time.
"We will hopefully get the credit we deserve. We came in difficult circumstances after losing the home leg, but were very positive and made a few changes, and on the night we were by far the better team.
"I'm really proud of what the players produced, but unfortunately we aren't the ones going to Wembley."
Stoke boss Hughes now has concerns about Arnautovic and Charlie Adam ahead of Saturday's fourth round FA Cup tie at Crystal Palace.
Arnautovic suffered a back injury after twice falling heavily following challenges from Liverpool defender Jon Flanagan, while second-half substitute Adam lasted barely half an hour before going off in the first half of extra time with calf trouble.
Adam was one of three players on the pitch from the last time Liverpool won a trophy, the League Cup final, also on penalties, when he missed in the shootout against Cardiff City in 2012.
Stoke right-back Glen Johnson was also in the Liverpool team that day, scoring one of their three penalties.
The only survivor from Kenny Dalglish's Reds team from 2012 still out there was Jordan Henderson, now the captain. Lucas Leiva, one of the Reds' penalty shootout heroes on Tuesday night, missed that Wembley final because of injury.
Stoke City boss Mark Hughes says Liverpool were "incredibly fortunate" to reach the League Cup final.