Bruce's men edged past Chris Hughton's side on Saturday thanks to a first-half penalty from midfielder Robbie Brady, although they played much of the match with 10 men after Ivorian striker Yannick Sagbo was dismissed.
Huddlestone signed from Tottenham on a three-year-contract earlier in the month, with Livermore moving from White Hart Lane on a season-long loan.
Both made their home debuts for Hull in central midfield, and Bruce was quick to credit their contribution to a determined team performance.
"It was just the icing on the cake for me, with a little bit of quality that you need at this level," Bruce told the club's official website.
"Tom Huddlestone and Jake Livermore are two very, very good footballers, and to have them in our midfield is terrific.
"Tom can only get better, he's such a wonderful footballer that the game is so easy for him, he makes it look so simple and obviously it's not.
"He's just a wonderful, wonderful player and he's had a wonderful debut alongside Livermore, who, in my opinion, suits him.
"The pair of them are a great pair, athleticism and dynamism, they can both be very proud of their debuts."