The TOM'S driver admitted on Saturday after qualifying sixth - best of the Toyota runners - that Honda's horsepower advantage made him pessimistic about the chances of overcoming his two main title rivals.
"I don’t know how to describe the feeling," reflected an emotional Cassidy. "I was crying on the in-lap. I’ve never done that before, I can’t remember the last time I cried.
"I think I sounded pretty stupid on the radio full of tears. It’s pretty special.
"My main worry today was Alex because this morning [in practice] he looked really fast. But we ended up having good speed in the race, so that’s good."
Speaking to Motorsport.com, he added: "Of course, it was a huge challenge given the situation [starting sixth with Palou on pole], I think that’s why I’m so emotional.
"I wasn’t in the favoured position but we made it work, which is amazing."
From sixth on the grid, Cassidy passed Koudai Tsukakoshi, Nirei Fukuzumi and chief rival Yamamoto to move up to third in the opening laps of the race.
The New Zealander then spent the remainder of the contest shadowing Mugen driver Tomoki Nojiri, who secured his first series victory in five years, and the New Zealander said that relatively early in the race he knew he was in a strong position.
"The only time I was worried was when I had [a lapped Juri] Vips in front of me," said Cassidy. "I got stuck behind him for a lap and a half.
"But the rest of the race was quite smooth. Nojiri-san had a nice pace, so I could follow him at a nice distance. I didn’t need to push to [catch] him, I just needed to go with him.
"I had a good image of the race [in my mind] and what needed to happen."
Cassidy moved across from Kondo Racing to Toyota's flagship TOM'S outfit at the start of 2019, linking up with the squad with which he took the All-Japan Formula 3 title in 2015 and then the Super GT title alongside Ryo Hirakawa in 2017.
But the 25-year-old described the Super Formula crown as "100 percent" the greatest achievement of his career to date.
He explained: "This one is kind of more special to me because now I’ve got the three [titles] in Japan. That for me is the most [special].
"Obviously it’s more personal because it’s one driver, and then the challenges of the new car, Honda versus Toyota, a new team... to come out on top is really special."