Cooper is injured but claimed he would have refused to play in Pretoria anyway because the "toxic" environment in the Wallaby set-up is "destroying" him as a person and a player.
However, it has been reported in Australia that angry senior Wallabies believe Cooper's comments are disrespectful to those who will take the field at Loftus Versfeld.
And Deans indicated the row had served to strengthen the determination within the Wallaby camp to extend an unbeaten run against the Springboks to six Tests.
The Wallabies will need that togetherness because they have never beaten South Africa at the high-altitude fortress of Loftus Versfeld.
"I don't think it's been a distraction at all, really," Deans said.
"It certainly hasn't been evident. We've had a good week of prep and we're just concentrating on playing and hopefully doing well in a Test match.
"That's the priority."
Australia have bounced back from successive defeats to New Zealand with home wins over the Springboks and then Argentina, although they had to come from behind in both matches.
Deans has taken the bold move to replace Cooper with Kurtley Beale, who will make his first Test start at fly-half after 30 in the full-back jersey.
Beale apologised to Australia supporters after his error-ridden display in the defeat to New Zealand but his application has impressed Deans.
"The (jersey) number might be new but his role within the game won't be," Deans said.
"Although his season hasn't been without challenge, Kurtley stepped up with his involvements on the Gold Coast (in their win over Argentina), making a difference when he was on the field.
"He's brought that enthusiasm forward with him since we've been in South Africa, has worked hard on the training track, and is excited about the opportunity ahead.
"He has good memories from some of his experiences over here."
It was Beale's last-gasp penalty in 2010 that secured Australia their first victory over South Africa in Bloemfontein in 47 years.
The Springboks have also made a change at fly-half, with Morne Steyn axed for 20-year-old Johan Goosen as one of four changes from the defeat to New Zealand.
South Africa opened their campaign with a home win against Argentina but Steyn has struggled for form as the Springboks drew with the Pumas and lost to both the Wallabies and All Blacks.
Goosen has been picked to bring a greater attacking thrust to the Springboks while Steyn, who plays his provincial rugby in Pretoria, has not even been included on the bench.
"I either back him 100% or not. That's the decision I had to take. This was very difficult, but I look at what the team needed first and then at the impact on the individual," coach Heyneke Meyer was quoted as saying on keo.co.za.
"At Loftus, where he has played well, it is a big call. But he accepted it graciously. I feel it is in his best interest that he doesn't play."
Andries Bekker and Eben Etzebeth both return at lock while Jaco Taute makes his debut at outside centre in place of the injured Francois Steyn.