The Ligue 1 side were powered to victory by a Lucas Ocampos brace, and further contributions from Dimitar Berbatov, Emmanuel Riviere, Fabinho and an own goal as they stormed into the semi-finals of the cup competition.
Monaco have not won the Coupe de France since 1991, but are one win away from matching their final appearance in 2010.
Ranieri said his side concentrated on getting the result, despite playing lower-tier opposition.
"A very good game, my players played very well. They were very focused... (and we did) not concede goals. Really, I'm very happy tonight," the Italian said.
Goalscorer Ocampos said he was pleased to help pile on the goals, but also stressed Monaco must regain their composure ahead of a Ligue 1 clash with Evian TG on Saturday.
"A win with many goals, we do not see that every day," Ocampos said.
"I am very happy with my work. I am going to enjoy (the victory) a little and quickly focus on Saturday's game."
Nabil Dirar put in the cross for Ocampos' second goal of the night, and Monaco's fifth, and the Moroccan midfielder was pleased his side could put on a show for the Stade Louis II faithful.
"It was a really good show, both for the players and the people who came to see us tonight," Dirar said.
"At the stage now we're in the semi-finals, we want to reach the final and win something this year."
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