Speaking on F1's Beyond the Grid podcast, Stoddart reflected on Alonso's rookie season as the Spaniard joined Minardi at the age of 19.
Alonso joined a team that was close to going out of business before Stoddart's European charter airline company bought it in December 2000, and turned up for his first race at Melbourne in the following year with minimal experience of the PS01 car.
Stoddart felt that Alonso immediately proved himself as a star in the making at Melbourne, where he qualified 19th in a car that had been hurriedly built over the winter, before finishing 12th ahead of Benetton's Giancarlo Fisichella.
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Before Alonso was set to leave the team for a Renault testing contract in 2002, Stoddart added that Alonso's searing pace at Suzuka cemented his opinion of the Spanish driver.
He explained that a misunderstanding over a warm-up "glory lap" may have put Alonso in the mood to go all-out in the 2001 finale, where he fended off Heinz-Harald Frentzen's Prost to finish a strong 11th.
"The first race [confirmed my view] - Melbourne 2001. A car that has had one straight line test for 50 kilometres. That's all it had, and he wrings its neck and brings it home in 12th place," Stoddart said.
"Now if you want another, it's Suzuka in 2001. In those days we still had the Sunday morning warm-up and it was a tradition that if a driver was leaving, you took all the fuel out of the car and you let them have a glory lap.
"That was all agreed with me. I was called to a team principal's meeting while Sunday warm-up was going on and for whatever reason, Fernando and his engineer had disagreed about him having a glory run.
"They put fuel in the car. So Fernando didn't really get his glory lap - very few times had actually Fernando complained, but that was one of them.
"He came straight to me and I didn't even know about it. He said, 'I didn't get mad, but they put fuel in my car.'
"I said, 'look, I can't do anything about it. I'm really sorry, Fernando, I did say to give you the glory lap'. But Fernando wasn't going to leave it at that.
"If anyone looks at the history of that race in Suzuka, Fernando put in 53 qualifying laps. If ever the world needed to know how good he was, look at the tapes!"
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Stoddart said that he first became aware of Alonso as a competitor in the 2000 F3000 season; the Australian's European Arrows squad with lead driver Mark Webber frequently battled against the Astromega-run car piloted by Alonso.
Qualifying on pole for the Spa finale, Alonso beat team-mate Marc Goossens by almost 15 seconds in a stunning performance at the Belgian circuit. Citing that race, Stoddart replied that he "pretty much" knew what he was getting with Alonso at the team.
"Being a competitor to him in Formula 3000, in 2000, I saw him drive at Spa that year, which was a masterpiece of driving," said Stoddart.
"He'd come to my attention throughout that year in 2000, but he was never out of my mind after that brilliant race at Spa.
"But Fernando, in those days and still even when he was with us, was very quiet and very unassuming. He just got on and did the job.
"I watched that race and what I saw in him that day was 'this is a guy that's destined to be world champion', even before he'd even got in an F1 car.
"And I wasn't wrong, except he should have had four [titles] - not two."
