Portugal captain Ronaldo joined Juve in a deal worth €112million (£98.5m/$131m), committing through to 2022 with the Serie A champions after ending a nine-year stay in the Spanish capital.
Ronaldo's arrival has largely been seen as an attempt to win the Champions League, the 33-year-old having helped Madrid to the title four times in the last five years.
The Italian giants were last kings of Europe back in 1996 and have lost in two of the last four finals, most recently when Ronaldo scored twice in Madrid's 4-1 success in Cardiff in 2017.
Allegri, though, denied that Juve's focus will be on Europe after the blockbuster signing of Ronaldo, who is yet to play for the club as he remains on holiday after the World Cup.
"Our objectives are always the same - we want to win all competitions," Allegri told reporters.
"Ronaldo is here to help us contribute towards our objectives, whether they be Champions League or Serie A."
Juventus maintained an unbeaten start to pre-season by coming from behind against Benfica in the International Champions Cup on Saturday, winning 4-2 on penalties after a 1-1 draw in New Jersey.
Wojciech Szczesny shared duties with new arrival Mattia Perin and Allegri denied he will seek to sign another goalkeeper after veteran Gianluigi Buffon left for Paris Saint-Germain.
"Absolutely not. We have three great goalkeepers and they will be the Juventus goalkeepers of the future," Allegri said.
"Buffon has made history with Juventus for 20 years. He has been the best goalkeeper, not only for Juventus but also the world, during that time.
"He made a decision to go to Paris and we wish him the very best."