Mulvey said some Roar players had looked overwhelmed, especially in the first half, but he did have words of praise for one of his charges - elusive Brazilian attacker Henrique, who bagged the first two goals of the game.
Referring to his nickname 'Biliquinha' (slippery fish), Mulvey predicted more standout performances from Henrique as he approaches his best form.
"What do they call him, the slippery eel or something? But he's a bit of an enigma because he's been injured for a good deal of the last couple of years and missed too much football, but we're slowly getting him ready," he said.
"He wasn't in his best position for us in the midfield in the first half and it did cause us a few problems, but once we put him central he scored within two minutes and I'm really pleased for him.
"But as you could see he was running on empty for the last five minutes before we brought him off, so we got him off in time so he should have a good rest now and be okay for next week."
Mulvey went on to explain his decision to start the Brazilian on the right side of the midfield, where he struggled to make an impact before moving to a central attacking role at the start of the second half.
"To be perfectly honest I expected Melbourne Heart to come and sit back and play on the counter, so my theory was that he wouldn't have to expend so much energy in the game.
"But when Melbourne Heart sort of flipped that over and they actually played very aggressively with a high press he was having to go deep for the ball and get forward, so it nullified the effect that I thought he would have because I thought it would be a very tight game in their half where we might have to break them down.
"So that was the reason why we did that in the first half, and obviously we made changes at half-time."
Overall, though, the Roar coach was unimpressed with the way his side allowed the Heart to play before the goals came.
"I'm actually not very happy with the performance today," Mulvey said.
"I thought the performance was not what is expected.
"There's a certain level of expectations about being a Brisbane Roar player and I think that today in the first half we were like rabbits in the headlights.
"We looked clueless at times in terms of how to play the ball out from the back and all it takes is just one or two people to be slightly off their game and it can really have an impact, and it spreads through the team.
"It is a good trait to be able to still win when those things are going like that, but I want to pay great credit to Melbourne Heart today, I thought they outplayed us in the first half and probably on the first half performance can count themselves a bit stiff today."
Meanwhile, Melbourne Heart manager John Aloisi refused to criticise his team after they went down 3-0 to Brisbane Roar, saying they had put in a competitive showing in spite of the final scoreline.
The former Socceroo also denied the Heart's poor form away from home was becoming a psychological issue for the squad.
Aloisi's team have not won in their last 16 matches outside Victoria, but the coach says it is not affecting the mental outlook of his players.
"Not at all, if you look at the players we had out there today, we had six new players from last season so they don't even talk about the away factor," he said.
"And the way we performed, it didn't look like we were too nervous about the away factor.
"Even when we went 1-0 down we kept on trying, so that's not going to play on our mind.
"This is a new season, fresh start. Out of the four games we've performed well in three, we've shown that we can compete with anyone, we've got players to come back in still, and if we keep on performing like that, then the results will come.
"You create chances, normally you'll put more away."