Seventeen-year-old man of the match Redmond set Blues on their way to a comprehensive 3-0 play-off second-leg victory over their Portuguese visitors, with the tie goalless from the opening encounter in Madeira last Thursday.
Hughton said: "I'm extremely proud. We knew it was going to be a very tough game. It was similar to the first leg where Nacional started very well. We took a little while to get into the game but once we did, I thought we were very good value for the win."
Blues now face the prospect of balancing at least a further six European matches with their quest for immediate promotion back to the Barclays Premier League.
"I think the important thing is that we are here, which of course brings us extra games, whether that is something we could do with or not," admitted Hughton
"But I think if you look at the atmosphere tonight and the performance, you had a team that very much wanted to go through and a full house that very much came to cheer the team on and, if you asked any of them if they wanted to go through, it would be an emphatic 'yes'.
"So we have to work around it. How far we can go? We don't know. But for as long as we're in it we will try and enjoy it."
Undoubtedly, the start of the show was winger Redmond - a Birmingham-born boyhood Blues fan and graduate of the Academy - who broke his duck for the club with a fairytale goal in what was his full home debut.
"He's a lad that we rate very highly here," said Hughton.
"You don't know how good he can be. He's a young man with a lot of potential and can play either flank.
"Certainly these performances won't do him any harm. It's very early days. He's very much on a high but we will have some lows and it's up to us to manage him. He's a young man with a lot of potential."