The five-time Ballon d'Or winner swapped life in the Spanish capital for Turin last month in a £100m deal, leaving a huge void to be filled at the Bernabeu.
Ronaldo was absent from the Juventus squad on Saturday evening as they slipped to a 3-1 friendly loss at the hands of former club Real in the United States, and Allegri is confident that the reigning European champions will remain a real force.
"Real Madrid is a great team," he said at his post-match press conference. "We're happy to have Cristiano, especially on the international stage and the experience that he brings to the club.
"However, Real Madrid will always be a competitive club, with or without Cristiano. It's going to be a pleasure to coach Cristiano Ronaldo, certainly he's one of the top players in the world next to Lionel Messi and I'm looking forward to the privilege of coaching such a fantastic player."
Ronaldo scored 450 goals in 438 appearances for Madrid, including 44 in 44 during his final season at the club.