The Cottagers secured a quarter-final meeting with Manchester United after just one day's rest following their league defeat of West Brom on Sunday.
Hodgson had spoken in the build-up to the game about his concerns over possible fatigue in his squad and the club pursued every avenue to have the game rearranged.
Ultimately, though, Hodgson made just two changes to his side - with Danny Murphy rested and Andy Johnson out with a knock - and they turned in a gallant performance.
Jason Scotland repeated his strike from the initial fifth round draw between the sides to put Swansea ahead but a subsequent onslaught yielded goals from Bobby Zamora and Clint Dempsey to seal a 2-1 win.
"I was really surprised with the players' energy tonight," admitted Hodgson.
"Their energy levels were fantastic. I thought we showed incredible energy just one day after playing a tough Premier League tie against West Brom and I can't praise the team enough for the way they prepared for this game and the way they've gone about their business from the very first minute.
"They also showed great character to come back from 1-0 down, albeit it was against the run of play."
Despite slipping behind Hodgson admitted he would have been highly annoyed had his side lost a game they dominated in the second period.
"There were a lot of goal chances and they were mainly at one end of the field. It was a very fast, very intensive game and I have to praise Swansea who did very well to live with us.
"You are always nervous when you go one goal down because you need to score two goals and you know how difficult two goals are to come by at any level of competition.
"But two goals, I think, was scant reward. Had we not won the game we'd have been sitting here feeling very sorry for ourselves after giving such a good performance."