Espargaro jumped Quartararo at the start when the Yamaha rider ran wide into Turn 2, with the former moving up to second.
After a brief battle went the way of Espargaro through Turns 5 and 6, Quartararo spent the next three tours stalking the Aprilia rider before launching another attack into Turn 5 on lap five.
However, Quartararo crashed and hit Espargaro off into the gravel, the Aprilia rider dropping to 15th before recovering to fourth at the chequered flag.
Quartararo, who crashed again on lap 12, was handed a long lap penalty for the incident to be served at Silverstone in August and apologised to Espargaro immediately after the race.
Espargaro did recover 13 points in the championship at Assen, bringing Quartararo’s lead down from 34 to 21 points going into the summer break – but admits he would have preferred to have finished 1-2 with the Yamaha rider as he feels he had pace to claim a second career victory.
“That’s difficult to know because I think today, I was able to win and Fabio would finish second,” he said when asked if he lost the win today or actually won in terms of the championship situation.
“This is five points, I recovered 13. If you think in [terms of the] championship it’s better, but I lose a victory.
“I’m pretty sure I could have won today. I have just one victory in my career, so I would prefer to recover five points and have the victory [than recover 13].
“If you are not calm it’s impossible to do many laps half a second under the previous lap record.
“I was aggressive, angry, super-angry because every time I saw my dash the lap times I was doing I was more angry because I knew it was impossible the others were doing their pace and I was catching.
“But at the same time, I was happy to be doing those lap times.”
Commenting on Quartararo’s crash, Espargaro believes there was no intent from the Yamaha rider and that he simply misjudged the braking zone for Turn 5 due to the strong feeling he has with his bike.
“I was very strong in that place and Fabio knew it,” Espargaro added.
“The reason why Fabio did that move is because his feeling with the bike is super-high, he’s able to close the lines a lot because he has a lot of feeling.
“He’s not a dirty rider, but his confidence is that high that he’s able to close the lines a lot.
“But today I was also super-fast, so I closed the line like him and we collided. He said sorry to me because he did a big mistake judging this braking.”
Espargaro also said he was able to recover so well after being forced off track because he had “nothing to lose”, but his superior pace to those around him made it easy.
“Today I had nothing to lose, and I think I’m going to sound arrogant, but my pace today was a little bit better than the rest,” he said.
“So, when you are around half a second [faster] it’s a lot easier because it means you are doing something very different than the rest.
“In the last chicane I was braking a lot later than everybody, in the last sector the speed I was able to carry was unbelievable. So, this is why it was quite easy for me.”