Robertson’s absence has been a big talking point for Cardiff fans, who have been perplexed as to why a player who cost the club a seven-figure fee when he joined from Manchester City in the summer of 2024 has not been used.
He was in Australia’s squad for their friendly matches in the United States and Canada earlier this month, but did not feature in either game.
“I think it’s fine for the supporters to talk about him in whatever way they want,” said Barry-Murphy.
“Alex is somebody who I know really well from long before he was at this club [when Barry-Murphy coached Manchester City Under-21s], so all I want for all the players is to be at their best.
“My duty is then to get them into that condition where they can compete against each other. But I have to be very fair and consistent in the way that I judge all the squad once they reach that level.
“That’s the same for Alex as it is for everybody else. If he was in the shoes of the other players, he’d want the exact same thing.”
Meanwhile, centre-back Dylan Lawlor could be back for Saturday’s League One trip to Bolton Wanderers having missed last Saturday’s 2-1 win over Reading with a groin injury.
Fellow centre-back Will Fish is also managing a knee issue, which limited him to 45 minutes against the Royals last weekend.
“Will Fish has an ongoing knee issue which is getting better, particularly when he hits longer passes,” said Barry-Murphy.
“He’s had some discomfort in his knee. But the amount of discomfort is getting less and less, so he’s making good progress.
“Dylan has had a good week of training so far. I think it’s important that he can do certain things that we want from later on this afternoon [Thursday] when we train, and then hopefully he can be available for Saturday.”