Morocco have faced criticism for their form despite progressing comfortably to the last eight, finishing top of their group with seven points out of a possible nine and beating Tanzania 1-0 in the round of 16 at the weekend.
Regragui has already warned supporters that top-ranked Morocco need to approach their matches with “humility,” but their performances have drawn widespread scrutiny for being overly cautious.
Speaking at a pre-match press conference, Regragui said the team remained confident despite feeling the pressure.
"We are still thinking the same way and have confidence in what we are doing," he told reporters.
"The players feel it, and we know we have to live up to it. The most important thing is that the fans continue to support us.
"We have the humility to believe that we can win this Cup of Nations," he declared.
"It’s a tournament that requires staying grounded, even if people do not want to understand that.
"But when you see the results and all the strong teams that have progressed, then you realise what you are up against.”
When Morocco last hosted the Cup of Nations in 1988, Cameroon knocked them out in the semi-finals, and the two countries have a long history of fierce contests.
"This will be a clash that will reverberate around the continent. Cameroon needs no introduction. We know it's going to be tough again,” Regragui predicted.
Morocco are unsure whether defensive midfielder Sofyan Amrabat will recover from injury in time after missing their last two games, but attacker Hamza Igamane is available after missing the opening fortnight of the tournament with injury, the coach said.