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Captain Smith and vice-captain David Warner spoke with CA chief executive James Sutherland before the start of play on Sunday and stood down from their leadership posts for the rest of the game.
"It was extremely difficult, that's no excuse for what you saw in the last 45 minutes," Paine said, having finished unbeaten on nine then apologised to Australian fans in the post-match ceremony.
"Unfortunately it fell apart in a really ordinary manner, which only rubbed salt into the wounds of what's been a horrible 24 hours for us.
"We are still the Australian cricket team and we are expected to put up a better effort than what we did.
"No one likes losing and no one likes losing in the circumstances that we have."
The wicketkeeper is expected to lead the team in the series finale starting in Johannesburg on Friday.
The 33-year-old faces an incredible challenge as he seeks to rally a new-look XI and deny South Africa their first home Test series win over Australia since the fall of apartheid.
Smith is unlikely to be the only enforced omission, depending on the result of CA's investigation.
"The one positive that may come of it, guys are going to get an opportunity to play for their country," Paine said.
"We can try to control how we are seen going forward by our Australian public and become the team that we want to become."
Smith, Warner and Bancroft were all booed to and from the pitch at Newlands.
The openers showed great composure in helping their side reach 0-57 before an unnecessary run out of Bancroft, completed with a direct hit from Proteas captain Faf du Plessis, ignited unmitigated chaos.
The margin was one run short of equalling Australia's biggest Test loss to South Africa, in terms of runs.
It shattered a 61-year record for the biggest Test victory at Newlands in terms of runs, bettering England's effort in 1957.
Man of the match Morne Morkel, who finished with career-best match figures of 9-110, and Keshav Maharaj were both on hat-tricks during the carnage."Everything happened so quickly," Morkel said.
Paine added more thoughts from the field after the defeat.
"The guys who travelled here, they deserved better than what we put up. That's all I can say on the matter at the moment."
He admitted it was tough to stay focused on the match with the shock of the incident still looming large.
"It was difficult no doubt but we said this morning that one of things we can control is to go out and compete as cricketers. So from a cricket perspective today was extremely disappointing.
"The way we folded in that last hour was very disappointing on top of what was already a horrible Test match.
"It was difficult for all of us and really challenging but down the track there's an opportunity for us to grow as a team and as individuals.
"We have to take some sort of positives out of it long term and turn ourselves into the cricket team we want to be.
"Smith and Bancroft are struggling, the enormity of what happened is starting to sink in."
Australia booed in embarrassing loss
Arriving and departing to boos from the crowd, Australia's cricketers endured further humiliation after being bowled out for 107 and losing to South Africa by 322 runs in the third test.
Australia was removed in less than 40 overs in its second innings on Day 4 at Newlands in Cape Town, failing to offer pride-restoring resistance and way off the winning target of 430.
With Smith and vice-captain David Warner stepping down from their leadership roles after discussions with their bosses before play started - and before the ICC ban on Smith was announced - Australia looked like a team with its morale shattered.
Read more: Steve Smith stood down as Australia captain
Smith and Warner played on Sunday but wicketkeeper Tim Paine took over as stand-in captain.
Warner top-scored for the Aussies with 32 and fellow opener Cameron Bancroft, also involved in the tampering plan, made 26 with an opening partnership of 57.
They were both booed as they arrived and then trudged off the field, as was Smith, who made just 7.
Read more: 6 Questions from cricket's ugly ball tampering bombshell
Away from the reputational damage suffered by Australia from its ball tampering on Day 3, Australia now trails 2-1 in the series with one test to go. Smith is banned for that last test because of his leading role in hatching a plan to cheat in the Cape Town game on Saturday.
Australia's proud record of having never lost a series in South Africa since 1970 is seriously under threat in Johannesburg next week.
Read more: The Aussie cheating crisis
South Africa's players had been told to maintain their focus on winning the test amid separate investigations by the International Cricket Council and Cricket Australia into the ball tampering which was planned, carried out and then botched by senior Australian players and Bancroft.
South Africa set Australia a huge task to win by making 373 in the second innings and then cutting through the Australian batsmen mercilessly.
Fast bowler Morne Morkel took 5-23 in Australia's second innings and nine wickets in the match in what is his last series in international cricket.
It was Australia's second-heaviest defeat to South Africa in terms of runs and its heaviest since 1970.
- AAP
