Juventus chairman Andrea Agnelli congratulated Inter on their Serie A triumph but promised his club would make every effort to win back the Scudetto.
After nine consecutive league titles, the long reign of Juventus was officially ended on Sunday as Inter wrapped up the 2020-21 championship.
Atalanta's failure to beat Sassuolo – that game finished 1-1 – meant Antonio Conte's Inter were home and dry with four games to spare.
Juventus, meanwhile, face a battle just to secure a top-four finish and Champions League football next season.
For all their defending of Andrea Pirlo, the first-time head coach has not made the impression that Juventus would have wanted this season.
They followed up last season's Scudetto by winning the Supercoppa with a win over Napoli in January, but it has been a largely disappointing campaign for the Turin giants.
"For ten years in a row we have won a trophy ... not bad, but the best will always be the next!" Agnelli wrote on Twitter.
In an apparent message to Inter chairman Steven Zhang, Agnelli added: "Well done Steven! Happy for you and proud of being your loyal opponent on the pitch and friend off the pitch. We’ll be back..."
Agnelli was one of the main protagonists behind the recent failed Super League project, with Inter and Milan having also been lined up to join that now apparently quashed competition.
Juventus sporting director Fabio Paratici mixed praise for triumphant Inter with reflection on what the Bianconeri achieved in past seasons.
Paratici told Sky Sport Italia: "I congratulate the club and Conte. We know that behind every success there is passion and sacrifice.
"We know how much effort we have given to win and be top of the class for 2,382 days. We have accomplished a historic feat, unique in Italian football and, probably, also in world football. Congratulations to Inter for a well-deserved Scudetto."