Football has struggled to find its feet in the cricket-obsessed nation of 1.4 billion people, with former FIFA president Sepp Blatter once calling India "a sleeping giant" of the sport.
Former West Ham and Derby defender Stimac was appointed coach in May 2019 and India briefly broke into the top 100 of FIFA's world rankings for only the second time in nearly three decades.
They are now 102nd, a spot below Kosovo, whose population is less than two million.
"A giant is definitely out of its slumber now," declared Stimac, before cautioning: "But I reckon it will take us another four years to enter the top 10 in Asia."
Under the former Croatia international, India qualified for the Asian Cup with three wins from three against Hong Kong, Afghanistan and Cambodia, scoring eight times and conceding once.
India's campaign starts on Saturday against 25th-ranked Australia and they have a mountain to climb in Qatar to get out of a group also containing Uzbekistan and Syria.
"We are far from being happy with the draw but it is what it is," the 56-year-old Stimac, part of the Croatia team that finished third at the 1998 World Cup, said in an email interview.
"With a very short time for preparation it's difficult to expect great things, but my even greater concern are the injuries to some of our key players.
"Anyway, we are going to give our best and make it very difficult for our opponents."
This will be India's fifth Asian Cup.
They were runners-up in 1964 in a tournament that had only four teams, but apart from that they have never got out of the group phase.
They have never reached the World Cup.
Fiery
Stimac's side lost 3-0 at home to reigning Asian champions Qatar in World Cup qualifying in November, underlining the task facing them in the coming weeks.
They also suffered friendly defeats to Malaysia and Iraq, before beating Kuwait 1-0 away in World Cup qualifying.
Stimac blamed the Malaysia and Iraq losses on "terrible refereeing".
"I hate talking about it but this area in Asian football needs to improve a lot," says the Croat, who has a reputation for his straight talking.
Indian sports administrations are regularly embroiled in controversy and in 2022 Stimac threatened to quit unless there were "drastic" changes in the domestic game.
"As a professional I have absolute freedom but I can work only with what I get from our decision-makers," he says.
In September Stimac called a news report claiming he consulted an astrologer to pick his team "a disgrace" and again hinted his time as coach might be coming to an end.
Role model Chhetri
Stimac says more than 20 youngsters have been brought into the squad during his reign "and our supporters are finally enjoying some exciting football watching their national team".
But it is an indication of the limitations of his squad that skipper Sunil Chhetri, at 39, remains India's biggest star.
Chhetri has plundered 93 international goals, putting him among the likes of Cristiano Ronaldo (128) and Lionel Messi (106) on the all-time list.
Stimac says the forward can bow out at a time of his choosing.
"We are not putting any pressure on him whatsoever," said Stimac.
"That's up to him."
"If he keeps enjoying his game with the same hunger and maintaining such brilliant fitness levels then we are there for him as long as it takes," he added.
"He is a proper role model for many Indian kids dreaming about becoming football players."