Youssef En-Nesyri's header late in the first half sent the Atlas Lions through to a last-four showdown with reigning champions France or England.
"We came up against a really great Portugal team. We're drawing on all we have, we still have guys injured. I told the guys before the match we had to write history for Africa. I'm very, very happy," Regragui told France's TF1.
Regragui, a France-born former Morocco international, had already made history of his own as the first African coach to take a team into the World Cup quarter-finals.
Morocco have now defeated three of Europe's strongest teams in Qatar -- beating Belgium in the group stage and Spain on penalties in the last 16 -- after drawing 0-0 with 2018 runners-up Croatia in their opening match.
Winger Sofiane Boufal hopes there is more to come.
"It's crazy. We're living and dream and we don't want to wake up. I have goosebumps," he said.
"Everything we have, we deserve. We work hard. It's not over. There's still the semi-final and god willing, the final."
Check the 2022 World Cup matches and statistics.
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