Berbatov scored the only goal of the game in the second half of extra-time to book Monaco's place in the quarter-finals and end the challenge of a Nice side that had been reduced to 10 men when Timothee Kolodziejczak was sent off after 48 minutes.
And Ranieri was quick to hail the former Manchester United forward's display as his first goal since joining from Fulham on the final day of the January transfer window kept Monaco's hopes of a first Coupe de France title since 1991 intact.
"I knew that this game would be difficult," Ranieri said. "Nice were better with 10 men than with 11.
"I made a lot of changes as we must play three matches this week [Paris Saint-Germain, Nice and Bastia].
"Dimitar Berbatov scored the goal. I asked him to play between the lines and he has done it well."
Monaco will face Olympique Lyonnais or Ligue 2 side Lens in the quarter-finals.