Team Orica-Scott's Brit crashed in the Blockhaus stage on Sunday with Team Sky's Mikel Landa, Geraint Thomas (Sky) and Wilco Kelderman (Sunweb). The latter two already abandoned the race due to injuries.
"It was a no brainier really," Yates said when asked about continuing in the classification fight.
He fiddled with his black Scott bike while his team-mates rode to the start of stage 13 in Emila Romagna on Friday morning.
"I lost four minutes and 40 seconds, but it's a long way to the finish, so we have many stages left. They are all pretty much mountain stages. So why would we change anything at this point?"
Yates sits 15th overall at 6-52 minutes behind the overall leader Tom Dumoulin (Sunweb). He lost around four minutes of that time when he crashed ahead of the Blockhaus summit finish. He closed the day with his wheel rubbing and frame broken, but determination intact.
"I was pretty lucky. I didn't get injured too much, because it was just my knees in my hip. I'm all good," Yates said.
"There are real stages coming, but if there's an opportunity to take some time... I reckon there a couple guys looking at each other so I will take that advantage and try to get away and if no one follows me, then I will be able to gain some time back."
On Saturday, the corsa rosa heads to the Oropa Sanctuary, sitting at the top of a 11.8 kilometre climb in Piedmont.
On Sunday, Yates and his rivals face an undulating stage to Bergamo that uses many of the climbs often featuring in the Giro di Lombardia.
After Monday's rest day, the final one, the race continues climbing all the way through the final time trial day next Sunday in Milan.
"There is still a lot to race for in this Giro," Orica sports director Matt White said.
"If we can win a stage and get the best young rider jersey, the Giro would still be a success for us."
"We may even have Caleb [Ewan] stay around to help Adam a bit with water bottles and so on. And you never know, we may need him for a chase in the stage like Oropa."
Watch: Giro d'Italia stage 16-21 preview
Yates is only a couple of minutes away from a top-10 spot and around three minutes behind Bob Jungels (Quick-Step Floors), the best young rider wearing the white jersey.
The 24-year-old from Bury, already placed forth last year in the Tour de France. This Giro, his first, is uncharted territory, especially since he has been unable to preview any of the Alpine mountain stages like the other leaders.
"Not at all," he said when asked how well he knows the final week's stages like the one over Stelvio.
"I was doing altitude camps and racing. I did not really have the time to see them, to be honest. It just didn't work out.
"[I rely] pretty much everyone for information. And there are plenty of resources online to check things out, so it's not like I have no information, but like I said, I'm taking it day by day to see how it goes."
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