Josip Tadic was awarded the goal on Sunday at AAMI Park which put Melbourne up 2-0 and ultimately proved crucial as the Heart ran out 3-2 victors.

Tadic was clearly offside when played through by Michael Marrone before he netted to give his side a two-goal cushion and a further goal from Fred was enough despite Besart Berisha's brace after David Williams was sent off on 67 minutes.

Mulvey said the assistant - most likely after seeing the replay - apologised to him when he questioned the decision.

"I asked him as he was running back and there was a break in play," Mulvey said.  "I said, 'mate, that was clearly offside wasn't it?' and he said, 'yes, I'm sorry'.

"It's unfortunate but these things happen. As I say, no excuses, no regrets.

"Melbourne Heart were the better team on the day because they scored three goals to our two."

According to Heart coach John Aloisi, referee Alan Milliner lost control during a frantic second half.

Mulvey said he had yet to see the Williams tackle on Ivan Franjic, which Aloisi felt warranted a red card.

The former Gold Coast United caretaker also spoke about his decision to change his side's system, which led to Berisha playing on the left for much of the first half.

The Albanian striker, last season's golden boot winner, was ineffective as Thomas Broich played centrally, but improved when shifted back to his best position late in the first half.

"I take responsibility for today. I changed the system before the game, worked on that during the week and it didn't quite work," Mulvey said.

"Mainly it didn't work because we had Berisha isolated on the left-hand side and he's much more dangerous central.

"We just went with a game plan where we tried to get Thomas free in that No.10 position and it didn't quite work for us.

"Possession-wise it did in the first 15 minutes or so, we got Shane (Stefanutto) out from the left full-back position we got him into some dangerous positions.

"But we didn't quite capitalise because Berisha's better central as he proved in the second half. I take full responsibility for that and we'll fix that during the week.

"I think that once we went back to the two wide and fast guys in the second half we looked a bit more dangerous and certainly more organised."