Terlich, 24, dressed as disgraced entertainer Rolf Harris and teammate Georgiou, also 24, dressed as a girl.
A photo of the pair posing together was posted on Instagram and has spread to other social media.
Melbourne Head Coach Paul Roos issued an “unreserved apology” to anyone offended by his players’ behaviour and has labelled their actions “unacceptable”.
“I find it hard to believe a couple of players could turn up like that and as a footy club (we are) completely unhappy with their behaviour,” he said a news conference on Tuesday.
In a joint statement, the pair admitted they had been insensitive, explaining: “We would like to apologise for our actions yesterday and the harm we caused. It was an insensitive choice and we are very embarrassed by it.
“Our thoughtless actions compromised the club and we sincerely apologise for that. We let down the supporters and everyone involved in the Club.
“We would also like to apologise to the AFL for our actions at a time when the attention should be on the teams playing finals.”
Image via Getty