The Portugal star left the Santiago Bernabeu for the Serie A title-holders in July, commanding a huge fee of €100 million (£88m/$117m) despite the fact he will turn 34 this season .
Ronaldo, still recovering from his involvement in the World Cup, did not feature as Madrid defeated Juve 3-1 in the International Champions Cup in Maryland on Sunday.
And Bianconeri boss Allegri knows the Spanish giants will remain a potent force in 2018-19, despite giving up their long-term talisman.
"Real Madrid is a great team," he told a post-match news 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."
Juve have enjoyed a productive off-season recruitment drive, bringing Leonardo Bonucci back from AC Milan and signing Joao Cancelo , Emre Can and Mattia Perin, in addition to the eye-catching capture of Ronaldo.
And, according to Allegri, no further new arrivals should be expected in Turin before the transfer window closes.
"The acquisitions are done by the club," he said.
"At this point I believe our club is very competitive and I'm looking forward to entering the season with what I have at my disposal."
Asked about Mehdi Benatia's first-team prospects following the return of Bonucci, Allegri said: "We have five [defenders] of a high level and we have a very busy season, so we're going to need all of them."