The Serie A side appointed the 53-year-old as coach after a disappointing season in which they were usurped by arch-rivals AC Milan in the league.
Inter missed out on their first official title of the season as they fell short of their city rivals in the Supercoppa Italiana and have shown very few signs of improvement in pre-season matches.
There have been doubts concerning Gasperini's capability to guide the club to success, but Moratti is convinced the former Genoa boss is the right man for the job.
"The fans have a strong sensitivity towards important problems and the club's difficult moments, sometimes they do not want to take it anymore and they express their disagreement," Moratti said.
"But I think we are still very strong, there could be doubts about the new system, but I think it comes naturally with the evolution of the team.
"Because of this, I am supportive of the coach, he will succeed with the tactical evolution he has been introducing and if it is not successful, our coach is smart and if he thinks it is right, he will change it.
"I am very confident about the league, while we will approach the Champions League game after game, given its difficulty."
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