Mazzarri's side sit fifth in the Italian top flight in the former Napoli coach's first season in charge at San Siro, five points adrift of fourth-placed Fiorentina.
A run of just one win in seven league games has damaged Inter's hopes of finishing fourth, while also allowing Verona to keep pace in the battle for the final UEFA Europa League place.
And, although Thohir, who purchased a majority stake in Inter in October last year, has urged fans to be patient, he insists that fourth place remains the goal for the 18-time Serie A champions.
"Compared to last season the team has improved," he told Republika Online.
"But the target remains fourth and I think that's plausible for us this season.
"I urge the fans to be patient – a business is not built in a few months. We're going to have to wait a few years.
"You only have to look at the model franchise in America to see that."
Inter's next Serie A clash comes against 10th-placed Genoa on Sunday.
