Pramac Racing rider Miller launched from second on the grid in the Emilia Romagna GP on Sunday, having missed pole position by a mere 0.076 seconds to Yamaha's Maverick Vinales.
The Aussie started the race strongly, taking the lead into the first corner before Vinales regained the ascendency.
But Miller soon began dropping back through the field, before surprisingly retiring from the race.
It was later revealed Miller's Ducati had unfortunately sucked up a visor tear-off strip from Quartararo that was covering the air filter.
"I am very sad because I had started well and we could have had a good race, we had all the right conditions to make it," Miller said.
"Unfortunately, it was nobody's fault, it was a very unlucky day because a tear-off entered the airbox."
Miller's teammate Francesco 'Pecco' Baganaia looked set for his maiden MotoGP™ win after taking a commanding lead from Vinales, but he crashed out with seven laps to go.
Vinales pounced to take the chequered flag, followed by Joan Mir (Suzuki) in second, with Pol Espargaro (Red Bull KTM) elevated to third after Quartararo (Petronas Yamaha) was penalised for exceeding track limits.
Miller returns to the track this weekend, as MotoGP™ moves to Barcelona for the Catalan GP at the Circuit de Barcelona-Catalunya on 25-27 September.
2020 FIM MotoGP™ World Championship Standings
- Andrea Dovizioso - 84
- Fabio Quartararo - 83
- Maverick Vinales - 83
- Joan Mir - 80
- Franco Morbidelli - 64
- Jack Miller - 64