Gasperini was appointed to the role in July but was sacked this week after a poor start to the new season where Inter suffered four defeats in five games.
Tuesday's 3-1 Serie A defeat at Novara prompted Inter president Massimo Moratti to publicly question the 53-year-old's leadership ability and by Wednesday night the manager had been ushered out the San Siro exit.
For his part, Gasperini said he cannot understand why Inter had lost faith in his preferred 3-4-3 system so quickly when they knew what his methods were before hiring him.
"I know that results determine everything," Gasperini told Secolo XIX.
"Inter knew that my system was 3-4-3.
"It is not that I do not know another system, but I believe that with this one, the team I coach play better.
"I explained this to Inter's chiefs three times, when I spoke with them. For this, I believe that the controversy about the formation was used as an excuse.
"If Inter did not believe in my work, why did they sign me?"
Gasperini, who landed the high profile post at Inter following a succesful stint at Genoa, added that his progress with the Nerazzurri was hampered by a lack of funds made available to him.
"With [Samuel] Eto'o sold, I wanted two players: Napoli's Ezequiel Lavezzi and Genoa's Rodrigo Palacio," he said.
"We could not spend any cash? Fine, but we could still sell Wesley Sneijder, Goran Pandev [who instead was loaned out to Napoli] and also Davide Santon, McDonald Mariga and Sulley Muntari.
"With two wide players and Diego Milito and Giampaolo Pazzini in the center, there were no problems: they could all play 30 games, in Serie A, Champions League and Italian Cup.
"Instead, came Diego Forlan, another champion, both on and off the field. I thought about putting him on the left wing and that way Sneijder could be a starter."
Gasperini also acknowledges that his inability to bring out the best from one of the club's prized asset in Wesley Sneijder was a real thorn in his side - ultimately this may have cost Gasperini his job.
"Sneijder is a champion, but I do not use a playmaker, so I tried to put him lower on the field, then higher and close to the goal," Gasperini said.
"I tried everything and nothing worked."
Inter have already appointed Claudio Ranieri as their new coach on a deal until June 2013.