Vasselon, technical director of Toyota Gazoo Racing Europe, put the Japanese driver's advantage over team-mate Brendon Hartley down to his renowned qualifying pace and local knowledge of the Fuji Speedway.
"He got everything right: the timing, the tyre preparation and the way he handled the circuit," explained Vasselon.
"We have seen at Fuji drivers who are used to the circuit have a small advantage. We see it in all teams: the fast guys are those who have been racing here a lot."
Kobayashi, who is also the team principal of the TGR WEC squad, admitted that he was surprised by his 1m27.794s lap aboard the #7 Toyota GR010 HYBRID Le Mans Hypercar, which was 1.5s quicker than the mark with which he took pole for the Fuji 6 Hours this time last year.
"The car felt really strong compared with practice, it improved a lot," said the Japanese driver.
"I was not expecting a lap time like that, and I was a bit shocked when I saw it."
Vasselon also conceded that Hartley, who took pole in the #8 Toyota at the Portimao WEC round in April, ran into balance issues during the 15-minute qualifying period for the Hypercar class.
"Brendon was not super-happy with the balance," he explained.
Hartley posted 1m28.418s to complete a Toyota 1-2 in qualifying on Saturday, but he was only a couple of tenths up on the third-placed Porsche 963 LMDh qualified by Kevin Estre.
Vasselon suggested that the Hypercar qualifying session that finished in light rain was a bit of a lottery and that some of Toyota's rivals weren't able to show their true pace.
"We got it right but with a bit of luck," he said. "We expected a lot more from Ferrari than they showed today, and Peugeot also."
The two Ferrari 499P LMHs took sixth and seventh positions on the grid in the hands of James Calado and Nicklas Nielsen.
Ferrari performance manager Mauro Barbieri claimed that "many details might be regarded as the culprit" for the poor showing in qualifying.
"The weather conditions were unpredictable, so maybe that led us to some set-up choices that didn't pay off in full dry qualifying," he explained.
He also suggested that the preparation of the team's Michelin tyres might also have been a factor.
Barbieri paid to tribute to Kobayashi's performance, saying the Japanese did "an astonishing job".
Peugeot driver Mikkel Jensen, who ended up 10th in the best of the French manufacturer's 9X8 LMH, claimed that the team had "failed to get the tyre to really work" over the course of the session.
Loic Duval ended up 11th in the sister car, but a full two seconds down on his team-mate after flat spotting a tyre and having to go for a second run on a new set of Michelins as the conditions deteriorated
