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The Atlas Lions, who had only progressed beyond the group stage once in five previous World Cup appearances, are the first African nation to reach the semi-finals following an incredible run in Qatar.
Having only succeeded Vahid Halilhodzic in August, Regragui has overseen victories over Belgium, Spain and Portugal to set up a last-four clash with reigning champions France.
Hadji appeared for Morocco at two World Cups (1994 and 1998), while he served as his nation's assistant coach from 2014 until earlier this year.
The 51-year-old is thrilled with what he has seen, telling L'Equipe: "Here in Morocco, it's crazy, what's happening for the national team is extraordinary.
"It's only been two or three months since Walid Regragui arrived in the national team. There was an upheaval with Vahid.
"The new coach was able to find the words and the way to bring out the best players and make a team with a lion's state of mind.
"The team plays with heart and an exemplary state of mind. With a coach like that, you can only flourish and work miracles."