Glenn Murray headed home a 95th minute winner as Albion ran out 2-1 victors to cement their second-placed spot in the Championship.
Following the triumph, Brighton moved eight points clear of third-placed Reading but Bruno insists the squad are taking it game-by-game.
He said: “It was a massive win for us, of course it will now make us believe that in other games when we are behind to still believe until the last minute. What I think is so important, even when you are not at your best, is to keep pushing and fighting for every ball, which we did and it showed the character that we have.
“I don’t think about being eight points clear in December, of course that is a great position to be in. But we cannot relax, we will not relax. This team is just thinking game by game to get every three points we can get.”
Solly March was introduced as a substitute in Saturday’s Birmingham clash and played a starring role.
The winger was influential for Albion last season before a knee injury last December ruled him out for the rest of the campaign.
With March now back and firing on all cylinders, Bruno hopes he will continue to have a similar impact in the new year.
He added: “He went through a really tough time with injury but I think his impact was unbelievable and we are so happy to see him playing football again because he is a very good player.
“We’ve got almost everyone back fit and that is so important because December and January are very big months.”
Having won four of their five matches so far this month, Bruno wants to see a strong end with home fixtures against Queens Park Rangers and Cardiff City to come over the festive period.
He said: “I think December is one of the toughest months in the league, it’s busy, it’s Christmas time, sometimes the pitches are tricky. After December there are only four months to go and you can see the end.
“I think it’s so important and we know that, so we will prepare right and be ready for these upcoming home games.”
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