Chief executive Nick Hockley believes permitting Usman Khawaja to wear a humanitarian message on his shoes would have set a "difficult" precedent for Cricket Australia to manage.
But claiming to support Khawaja's desire to express himself, Hockley indicated CA would review the situation between the first and second Tests of Australia's series against Pakistan.
During Tuesday's training session, Khawaja was spotted with the phrases "all lives are equal" and "freedom is a human right" emblazoned on his shoes, in solidarity with the victims of warfare in the Middle East.
But the ICC prevented Khawaja from sporting the phrases in the first Test in Perth, on the grounds that players are prohibited from displaying personal messages on their uniforms.
In an Instagram video, Khawaja confirmed he would lobby the ICC for an exemption, and doubled down on his stance while speaking to broadcast media on day one at Optus Stadium.
CA has backed the ICC's stance from the outset.
"Absolutely we want to support all our players who feel strongly about certain things to express themselves," Hockley told radio network SEN.
"But when you're playing cricket for your country, when you're out there representing your country, I think those (ICC) guidelines and regulations are in place for good reason."
In 2020, West Indies players began wearing the Black Lives Matter logo on their collars after the death of George Floyd, an African-American man killed by Minneapolis police that May.
The move was announced just over a month after Floyd's death, and Hockley believed it was natural that any similar exemption for Khawaja would take time for the ICC to approve.
"The main thing is there are processes available, but it needs to be done in the right way and with due lead time," he said.
"It's about precedence and about having some level of control.
"People are representing their country in cricket matches. If it just opened up then, it'd be very, very difficult.
"If you did get into a situation where people were putting forward things that are inappropriate, then you don't have control."
Hockley has already discussed the situation with Khawaja.
The CA boss is open to reviewing the situation in the week between day five of the Perth Test and the beginning of the Boxing Day Test in Melbourne.
"Everyone's now really focused on the cricket, and it's something we'll sit down next week and talk through," he said.
"That's best done outside of a Test match."
Taping over the messages on his shoes, Khawaja wore a black armband while batting against Pakistan in Perth on Thursday.
Hockley was unsure whether the armband would be interpreted as a personal message, and potentially grounds for sanction, by the ICC.
"That's something for the ICC and the match referees," he said.
Khawaja scored 41 runs in the first innings before edging to Sarfaraz Ahmed just after lunch on day one.