It was the third time this season that the Roar have lost to the Jets, who move up one place in the A-League table to eighth.
The 58th minute penalty came when Japanese referee Takuto Okabe ruled that Roar defender Shane Stefanutto had brought down a charging Josh Brillante inside the area, even though it appeared the foul may have started outside the box.
"It was never a penalty," Mulvey told reporters after the game.
"It was outside the box for a start and to say the boy fell would probably be fair."
Though supportive of the idea of the exchange program which brought the J-League referee to the A-League, the Roar manager questioned its timing.
"The thing that is disappointing is that we find a time to do it when points are at a premium, and you ask a referee... I thought the referee was very good today, he let the game flow, but I thought he missed a couple of things.
"And when you don't know players, and their traits, and it was clearly outside the box, the penalty that he gave, and I thought there was a penalty on Matt Smith when he was going for a cross from a free kick."
Regardless of the gripes about the officials, Mulvey was prepared to shoulder the blame for the loss.
"Not good enough at all," he said of Brisbane's performance.
"If we're supposed to be a team that's champions in waiting, then we need to have a good long look at ourselves.
"I take full responsibility.
"I'm the person that puts the team on the park, chooses the tactics, makes the substitutions; so today is my full responsibility.
"But what I'll promise to Brisbane Roar fans is that I'll fix it."
Asked what he got wrong specifically, Mulvey pointed to a number of factors.
"Lots of things," he said.
"Didn't move the ball quickly enough, didn't get between the lines quickly enough, didn't look forward quickly enough, took too many touches and against a team that came to spoil, rather than play, and catch us on the counter attack, we're used to that here, and we got done over."
