The Tigers had not beaten the Reds in 16 previous encounters but claimed the win thanks to strikes from Jake Livermore and David Meyler and a Martin Skrtel own goal, while Steven Gerrard scored for the visitors.
The result was the perfect way to bounce back from a 1-0 home loss to strugglers Crystal Palace last time out and saw the Tigers rise to 10th in the table with 17 points from their opening 13 games.
Asked if it was the best result of the season so far, Bruce told Sky Sports: "It certainly has to be.
"For me personally beating Sunderland and beating Newcastle (are the best results) but it's another three points.
"But what it does do, it gives the players a bit more belief. Some of them haven't played a lot in the Premier League and what they need is results like today to give them that belief that they can play at this level.
"We disappointed ourselves last week so you needed a response. So it was a big game in that respect.
"Sometimes when you play against the big ones, there's no real motivation from me - they know they have to play well if they want to try and get a result."
Owner Assem Allam's proposals to rebrand the club as Hull Tigers has led to the formation of an opposing "City Till We Die" fans' group and some heated exchanges between both camps.
Bruce added: "Of course we've got to sit around a table and say 'Look the one thing we can't allow is to fester on and it becomes a negative rather than a positive'.
"I thought the atmosphere today was terrific because of it. Now whether he's doing that on purpose I'm not so sure but certainly we have to address it and make sure that it doesn't become an issue."