The 19-year-old Swiss Dupasquier is in “very serious condition” in hospital in Florence after a terrible accident during qualifying for the Moto3 race.
Quartararo admitted that it was difficult for him to regain his focus initially when the post-accident delayed FP4 session finally began, but he clinched pole with a new Mugello lap record of 1: 45.187 minutes.
“This morning when I do 1m45.6s and Pecco. have seen [Bagnaia] was two tenths faster, I said ‘wow, in qualifying we can be almost 44 and 45 low,’ ”said Quartararo.
“And in fact I made a mistake on my first lap on the first run and here I have the feeling that only the first lap of the tire on our motorcycle is good.
“But it’s probably one of my best laps of all time and I want to dedicate it to Jason.
“I hope we have great news.”
Ducati rider Bagnaia, who qualified second, said Friday he expected at least seven or eight riders to battle for victory in Sunday’s 23-lap Italian GP.
Quartararo expects a similarly chaotic race but is confident that Yamaha will be there from the start as it now has a front holeshot device.
“Yes, actually too many drivers with good pace,” he said when asked about the competitiveness of the field after the race in FP4.
“But Pecco, Johann [Zarco], [Alex] Rins, I think we have a really great pace and I’m pretty happy with the front-end equipment we have.
“At the beginning of FP1 I had a bit of trouble using it, also weird when braking for the first time because you feel like your bike is super low.
“But I got off to a really good start in qualifying and we will gain confidence step by step and I have the feeling that we can do something big for tomorrow’s start.
“Conditions will change. Here we know that after the Moto2 race it is the only track on which the conditions change significantly. “
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Quartararo also commented on Marc Marquez’s qualifying tactics against his Yamaha teammate Maverick Vinales in Q1, believing the Honda rider’s actions were “borderline”.
Vinales has since said that Marquez had nothing to do with his Q1 exit while the Honda driver apologized for his actions.
“I was at the limit, to be honest,” said Quartararo of Marquez’s tactics. “I had the same in Malaysia in 2019, but not so much.
“For me, I see it as a bit borderline because Maverick came into the pits, but he [Marquez] came into the pit.
“That’s not my job, I don’t want to judge anyone. But it was strange to see this picture. “