Berbatov was a deadline-day loan signing from Fulham as Ranieri sought to fill the significant void left by Radamel Falcao's knee injury.
He made his debut as a substitute against Paris Saint-Germain at the weekend, and he stepped off the bench again to net the extra-time winner which finally ended the resistance of ten-man Nice on Wednesday evening.
Ranieri told L'Equipe: "I made a lot of changes because we have to play three games this week and Dimitar Berbatov scored the goal. I asked him to play between the lines and he did that well."
Berbatov's was the only goal Monaco could muster despite Nice losing Timothee Kolodziejczak in the 48th minute.
"I knew the match would be difficult - I always said so," Ranieri said. "We had practised penalties in the morning.
"Nice were better with ten than with 11. I had noticed they had almost exactly the same home record as us and, watching their game against Marseille, I saw a team who are very dangerous on the counter."
Monaco will face the winners of Thursday evening's tie between Lyon and Lens in the last eight.
Puel proud of Nice efforts
Ranieri's opposite number Claude Puel was proud of his players despite their eventual defeat.
"There is a lot of frustration," he said. "My players had to be heroes - they gave everything. With one man short, we controlled the game well and deserved a better outcome."