The Atlas Lions, one of the pre-tournament favourites, became the latest high-profile team to bid farewell to the tournament as they spurned a few goal-scoring chances and were punished by South Africa at the Laurent Pokou Stadium in San Pedro.
Evidence Makgopa scored against the run of play in the 57th minute before Teboho Mokoena wrapped up the win in stoppage time, curling home a free kick awarded for a last-man foul that led to the dismissal of Morocco midfielder Sofyan Amrabat.
"We could have maybe settled the game in the first half but, at this level, you get immediately punished for any chance you waste," Regragui told beIN Sports.
Morocco had a golden chance to draw level with five minutes remaining when they were awarded a penalty for a handball but Achraf Hakimi blasted his effort against the crossbar.
"The penalty hurt us a lot, and surely we didn't do everything that is required but I take full responsibility," Regragui added.
Morocco were hoping to win their first Cup of Nations title since 1976, having made history at the 2022 World Cup after becoming the first African team to reach the semi-final.
However, their displays have been far from convincing in the Ivory Coast, and they were affected by the absence of some key players against South Africa, including injured duo Hakim Ziyech and Sofiane Boufal.
"We will learn from this unexpected stumble ... this is a disappointment for our fans who supported us a lot," Regragui said.
