The Roar's all-or-nothing approach has resulted in 19 straight games without a draw, but unfortunately for Mulvey the latest of those was a defeat thanks to a late Jordan Elsey header.
Returning striker Besart Berisha found the net after coming on as a substitute, but another of Brisbane's foreign stars, Thomas Broich, could be in doubt for the next match after suffering from a cork.
Brisbane were forced to play with 10 men from the 41st minute when right-back Diogo Ferreira received the second of his two yellow cards.
Even with a numerical disadvantage, the hosts improved in the second term, drawing level thanks to Berisha's well-taken strike in the 80th minute, and then pushing for the win.
This desire to fight till the death is ingrained in the club, according to Mulvey.
"The belief at this club is that we play to win every game," he said.
"And I think that the courage my players showed in the second half was absolutely magnificent.
"We got the equaliser and we still had that belief that we could go on and win the game.
"Their goal is some cross from the left hand side and it's some header by the big fella so, good luck to them, they go home with the points."
Mulvey hinted that he was unhappy with some of the refereeing decisions in a first half which Adelaide had the better of.
United's first goal came after they had been awarded a penalty for a Michael Theo foul on Jeronimo Neumann.
Though the Argentinian missed the spot kick, Theo was unable to hang on to the ball and Jeronimo followed through to dab it into the net.
"We had some unfortunate things not go our way," Mulvey said of the first half.
"And we crafted a couple of chances.
"I had a little word with the referee at half time, and what was said between him and I will remain that way."
Brisbane's German playmaker Broich received plenty of attention from Adelaide's defenders, and the Roar coach said he was having some difficulties after taking a knock.
"Thomas was struggling a little bit at half time with a whack that he got and he was heroic for us in the second half because he knew that he could still do enough, but it's very difficult to keep performing when you keep getting whacked," he said.
"He's got a cork, and I anticipate that might be a couple of weeks as well, but you never know with Thomas, he's a marvel, so he may recover a lot quicker."