The Rabbitohs' pair returned to their homes on Friday afternoon, after Gray had urged people to take medication only as prescribed.
The pair spoke to media at St Vincent's Hospital, four days after being admitted from overdosing on painkillers assigned to relieve them of post-season surgery.
Flanked by ashen-faced friends and family, both players emerged to thank staff before saying their experience should be a warning to others.
"We'd like to apologise to all our family and friends for the last few days. We know it hasn't been easy," Gray, 21, said.
"We've learnt from our mistakes and we hope that everyone can learn from our lessons, not only rugby league players, but people in general.
"Just take prescription medication as it is on the prescription box."
A similarly contrite Walker admitted he and his teammate had erred.
"I'd like to say sorry to our friends and family for the mistake we have made," Walker, 20, said.
"It's a lesson we have learned and we hope everyone can take a lesson out of this."
The pair did not take questions from the media.
Rabbitohs chief executive John Lee said the club accepted some responsibility in relation to pushing their players to return quickly from injury, and had been instructed by their board to conduct a full investigation.
While some details remained murky, he ruled out the use of illicit drugs.
"There are necessary pressures that are applied so that players are able to take the field," Lee said.
"For us, we own that that is a problem not only at our club, but probably in some other clubs.
"We will take the responsibility to put in better protocols, to make the right changes and to have the right levels of education so as we can prevent this incident from occurring again."
Lee, who sits on the Australian Sport Commission, also urged the Rugby League Players' Association and the NRL to discuss the testing of hair follicles in a bid to clamp down on prescription
medicine abuse.
"It's fair to say that prescription medication is not a rugby league issue only," he said.
"They are an issue across all competitive sport, and it's something that we need to face fair and square."
"I can confirm that our chairman (Nick Pappas) and our coach Michael Maguire, we would like to be at the forefront of a new trial through the use of hair follicles.
"It is something that takes place in other parts of the world, and we think it's time that there is greater monitoring, as well as education, so as this incident can be prevented."
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