"It's still quite difficult," Quintana said when asked if he could win in Milan on Sunday.
"Tomorrow will be the decisive stage."
Quintana, the 2014 champion who rides for Movistar, finished nearly eight and a half minutes behind Spanish Team Sky rider Mikel Landa who soloed over the finish line following a 191km ride from San Candido to the summit finish at Piancavallo.
But it was enough to give the Colombian, who saw Dumoulin make a "rookie mistake" and struggle throughout the fourth of five days in the mountains, the race lead two days before the 100th edition finishes.
Dumoulin – bidding to become the Giro's first Dutch champion – dropped to second overall at 38secs with Italy's two-time champion Vincenzo Nibali (Bahrain) now third at 43, 10 secs ahead of resurgent Frenchman Thibaut Pinot (FDJ).
With a final day in the mountains on Saturday's 20th and penultimate stage from Pordenone to Asiago, Quintana now has his work cut out.
Especially as Sunday's final stage is a mainly flat time trial over 29.3km from Monza to Milan, and Dumoulin was nearly three minutes faster than him on the 10th stage time trial last week.
"We have to try and take more time from Dumoulin tomorrow," said Quintana. "He is much stronger in the time trial."
Nibali, who lost 2min 07sec to Dumoulin on the stage 10 race against the clock, agreed: "We have to give it everything tomorrow, we have to take as many seconds as possible before the time trial.
"Dumoulin is still in contention, but so are a few others."
Sunweb team leader Dumoulin produced some valiant efforts trying to save his pink jersey this week, including a brave solo climb over the formidable Stelvio climb following an embarrassing, unscheduled toilet stop.
But a day after sparking a spat with Quintana and Nibali, the Dutchman was given payback.
Although he shook hands with Nibali before the start, Italy's two-time winner was quickly involved when Movistar put the pedal to the metal on the descent of the first climb.
It caught Dumoulin cold, and he admitted: "I had bad legs from the start and I made a rookie mistake at the beginning, sitting at the back of the bunch on the downhill.
"Then Bahrain and Movistar split the bunch and I was in the second group and needed, with my bad legs, to go to the maximum to come back, in the middle of the stage. So that was really unnecessary."
Throughout the stage, Dumoulin was in danger of losing the lead after being isolated prior to the final, 15.4 km climb to Piancavallo.
Landa, who had been part of an earlier breakaway that built a lead of nearly 10 minutes, made amends for his runner-up finish to Tejay Van Garderen on Thursday when he attacked Rui Costa 10 km from the summit to solo over the finish line well ahead of his Portuguese rival.
"I was very emotional at the finish because I've had a tough few months, and earier in the Giro when we crashed," said Landa, one of several riders brought down, alongside teammate Geraint Thomas, by a police motorcycle on stage nine.
Meanwhile, as Dumoulin's pink jersey grip continued to slip, Pinot boosted his chances of a podium finish for the second successive day by attacking Nibali and Quintana's group 6km from the finish to close to within 10secs of the Italian.
Four riders are now within one minute of Quintana, setting the scene for a spectacular final day in the mountains.
"It's a particular situation because it's not just victory being decided, it's all the podium places and positions," added Quintana, who now has the job of trying to control Dumoulin, Nibali and Pinot.
"I expect Nibali to attack, but whoever attacks first, all the others will follow."