Dumoulin's overall lead was drastically reduced in the race's toughest stage after Nibali and Quintana capitalised on the Sunweb rider's stop to answer the call of nature at the foot of the last of three major climbs.
Defending champion Vincenzo Nibali of the Bahrain-Merida team won the stage, which crossed the Mortirolo and Stelvio passes.
"I just had some problems," Dumoulin said. "I started to feel it in the downhill of the Stelvio and I had to stop.
"Back on the bike, I decided to fight and draw conclusions after the finish. I'm still in the Maglia Rosa (leader's pink jersey) but I'm above all very disappointed.
"This is not something I was hoping for and I also don't think it shows my level at the moment.
"I had good legs. But there's nothing to do about it. I'm disappointed with myself that I lost two minutes while not having bad legs or anything but just having a problem."
Becoming the first Italian rider to win a stage in this year's race, Nibali edged Mikel Landa of Team Sky in a two-man sprint, with 2014 champion Nairo Quintana (Movistar) crossing third.
Dumoulin finished more than two minutes back but maintained a 31 second lead over Quintana, while Nibali moved up from fourth to third overall, 1min 12sec behind.
At the start of the stage, a moment of silence was observed for the victims of the suicide attack at an Ariana Grande show in Manchester, England, plus the death of ex-MotoGP champion Nicky Hayden, who was hit by a car while training on his bicycle.
Stage 17 on Wednesday is a 219-kilometre leg from Tirano to Canazei featuring three categorised climbs, followed by an even tougher stage through the Dolomites on Thursday.
The 100th Giro ends Sunday with an individual time trial in Milan that should favour Dumoulin.
“It's the victory of a complete rider," Nibali said. "I had to be consistent from start to finish in a long and difficult stage. At the end, I had to be an aggressive climber, a good downhill rider and a sprinter.
"I wasn't thinking of delivering the first stage win for Italy. I knew it would be very difficult to make it. I'm very happy I won with the help of the team.
"I arrived [at the finish] really tired. I'm closer to Dumoulin on GC now. There are more difficult stages to come but Dumoulin also has a time trial to his advantage in Milan.”