Hughton hails 'character' of FA Cup heroes Brighton & Hove Albion
The Seagulls trailed 2-0 until late, late goals from Jurgen Locadia and Solly March forced the game into extra-time.
With no further goals in the extra half-hour, Albion once again fought back after missing their first spot-kick to win 5-4 on penalties and book their place in the final four.
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Hide AdHughton said: "The first word that comes to mind after you've won it is character.
"Credit to Millwall. What they wanted to do they did very well today.
"Although we had lot of possession they restricted us to minimal chances and I can't think of too many clear-cut chances that we had in that time.
"At 2-0 down you're out of the competition. I felt that we could get one back because of the balance of play and how much possession we were having, but to get two back in that last period shows great character.
"Missing the first penalty and then them scoring their first three also shows wonderful character and composure from a group of players that desperately wanted to go through."