But the towering Socceroo and Swansea City defender was never going to apologise for scoring his first professional double - especially not as stand-in skipper in a major cup match.
Burgess was the hero for Swansea, scoring twice including a 97th-minute winner as they came back from 2-0 down to beat Postecoglou's Nottingham Forest 3-2 in the third round of the League Cup.
Pressure has only intensified on Postecoglou since, with Forest (1-2-4) sitting 17th in the Premier League.
"Obviously you're never going to try and not score, of course," Burgess said.
"But look, I've full faith in Ange and what he does, and all the players he's helped in his career and things like that - that he'll do great at Forest.
"And look, it takes time. Rome wasn't built in a day as they say. So - every faith he's going to do well."
Burgess added, jokingly "thanks for making me feel bad", before noting he hoped Postecoglou and assistants Mile Jedinak and Nick Montgomery could succeed.
"Look, he has some great people there as well - obviously all the other coaches he's got that have come across as well. And it was great to see them on the night. I was really looking forward to it," Burgess said.
"It was good, from my point of view, to score a couple goals. But not so great from their point."
Burgess has been loving his time at Swansea, believing his move "couldn't have gone better" after he signed from Ipswich Town.
Regular game time has also been crucial as Burgess, set to play in coming friendlies against Canada and the US, prepares for the Socceroos' World Cup campaign next year.
Burgess is thriving in the crash-and-bash intense English Championship, where 17 Australians are plying their trade.
That includes young guns Nestory Irankunda (Watford) and Adrian Segecic (Portsmouth) and defenders Lewis Miller (Blackburn Rovers) and Hayden Matthews (Portsmouth).
When asked if he had any tips for his fellow Socceroos on how to handle it, Burgess joked: "I'm not telling them nothing, to be honest, because they're competition. So they're getting nothing off me."
He then noted it was a "relentless" and unpredictable league for players to become accustomed to.
"There's a lot of crazy results going on, and that's the league in a nutshell.," he said.
"Really, it's just: expect the unexpected, and the hardest part about the Championship is to try and find consistency, really.Â
"So my advice to them would be try and find that consistency as best you can in your own game and hopefully that feeds through their teams and they have successful seasons - but not against us."
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