Rafa Benitez's men were well off the pace set by eventual winners Juve, coached by Antonio Conte, and Roma but comfortably finished third in Serie A to book a place in the Champions League play-offs.
However, with Conte having parted ways with the Turin club on Tuesday and former AC Milan boss Allegri now in charge, Mancini believes that Napoli will step up to take the Scudetto race by storm in 2014-15 with the Bianconeri to falter.
"It's possible that among the Juve players right now there is a fair bit of confusion," the former Inter boss, who denied he had been approached to replace Conte this summer, told Sky Sport 24.
"For Allegri will be difficult, but he will be proud that he gets the opportunity to coach such a club. He will not need a huge amount of squad strengthening to compete for the title, although this year I have different winners in mind: Napoli.
"They excite me more. Benitez knows the team and they intend to strengthen. They will fight with Juventus, Roma and perhaps AC Milan."
Under Walter Mazzarri Inter finished fifth in Serie A last season and, again, Mancini - who brought domestic success to San Siro - cannot see his former team battling at the top of the table in 2014-15 unless they bolster their squad immensely.
"I do not think Inter can be one of the favourites, but this will depend on who they sign or sell in the transfer market," he added. "But it seems that project is a long term one."