"It's obviously unacceptable and I'll have to learn from that," Collingwood said. "I made a mistake."
Collingwood was fined 1,000 pounds (US$2,000; 1,440 EUR) by England management later Tuesday.
Collingwood visited the club in Cape Town after England had lost to Australia on Friday by eight wickets.
"(I) had a beer and thought 'I need to get out of this place,"' Collingwood said.
Britain's The Sun newspaper, which reported the story in its Tuesday edition, said Collingwood left in the early hours of Saturday morning.
England lost Sunday to South Africa by 19 runs, and was again defeated Tuesday by New Zealand by five runs. The third straight defeat means England is now unlikely to advance to the semifinals.
Collingwood captains England in one-day and Twenty20 matches. Michael Vaughan, the England test captain, relinquished the limited overs leadership after England's disappointing performance in this year's World Cup.
Allrounder Andrew Flintoff was stripped of the vice captaincy during that tournament after a widely reported drinking session in March on the eve of a match.