Against Belgium, man of the match Ziyech showed what the team was missing in a brilliant performance that helped Morocco to their first World Cup victory since beating Scotland 3-0 in 1998.
"He is incredible, the spirit he has, coming back to the national team," a jubilant Regragui said.
"A lot of people talk about him, say he is crazy and difficult to manage, that he can't help the team.
Ziyech had Morocco's first shot on goal in the second half, and was allowed to move freely between the lines in the front third, tormenting the Belgian defence.
Another substitute, Abdelhamid Sabiri, struck the shot that touched captain Romain Saiss on its way in for the first goal.