Pidcock made a move on the final climb and Vingegaard was the only rider able to go with him.
“It is hard to describe the disappointment to be honest. I felt like today was my day,” said Pidcock.
Vingegaard said: “It’s my son’s birthday – he’s one year old today so I wanted to win for him.
“We worked all day for it and to not get the chance is obviously a big shame.”
Prior to stage 11, riders had met for a safety meeting, while the Professional Cyclists’ Association called for better security at an event at which the Israel-Premier Tech team have been targeted.
On stage five, the Israel-Premier Tech team were held up by protestors holding pro-Palestinian flags and banners.
Italian rider Simone Petilli, who competes for the Intermarche-Wanty team, fell on stage 10 when protestors ran on to the road.
Petilli wrote on social media before Wednesday’s stage: “Please, we are just cyclists and we are doing our job, but if it will continue like this our safety is not guaranteed anymore, and we feel in danger! We just want to race.”
Following stage 11, Pidcock said: “Putting us in danger isn’t going to help your cause.”
The UCI statement added that it “expresses its full solidarity and support to the teams and their staff, as well as to the riders” who they said “must be able to exercise their profession and passion in optimal conditions of safety and serenity”.
Vuelta organisers said in a statement that the race “respects and defends the right to peaceful demonstration” but “cannot tolerate any acts that put at risk the physical safety of the participants or any member of the race caravan”.
Israel-Premier Tech ruled out pulling out of the race, saying the team “remains committed” to the event.
The team added: “Any other course of action sets a dangerous precedent in the sport, not only for Israel-Premier Tech, but for all teams.
“Israel-Premier Tech has repeatedly expressed its respect for everyone’s right to protest, as long as these protests remain peaceful and do not compromise the safety of the peloton.
“We thank the race organisers and the UCI for their continued support and co-operation, as well as the teams and riders that have expressed their support both publicly and privately and, of course, our fans.”
Israel’s military launched a campaign in Gaza in response to the Hamas-led attack on southern Israel on 7 October 2023, in which about 1,200 people were killed and 251 others were taken hostage.
At least 63,633 people have been killed in Gaza since then, according to the territory’s health ministry.
Stage 12 of 21 on Thursday is scheduled to take place over 144.9km from Laredo to Los Corrales de Buelna.