Pierre-Emerick Aubameyang's 24th goal in as many Bundesliga appearances this season gave Dortmund an early second-half lead but Thomas Tuchel's team could not make their superiority weigh any more heavily.
Left-back Thilo Kehrer struck 13 minutes from time, netting a first goal of his senior career with aplomb, and Dortmund were the side under pressure from that point as the noise levels ramped up at Veltins Arena.
In stoppage time, centre-back Bartra appeared to misjudge a headed clearance and the ball struck his outstretched arm.
Schalke were furious referee Felix Zwayer failed to point to the spot, with head coach Markus Weinzierl sent to the stands for his protests, but Burki felt his team-mate's infringement was accidental and deserved to go unpunished.
"I saw that the ball went to his hand but I think he could not do anything. It was so fast," he said. "He couldn't take the arm away."
"We are not happy. We were in front 1-0, a beautiful goal. It started from behind when the ball was in my hands," he said.
"They had not many more than one chance and they scored. At the end they made a lot of pressure on our goal in front of their fans.
"It was difficult until the end but we are not happy about this result. We have dominated the game. At the end it looked closer than it was.
"We have to look forward. We played good. We had chances to win this game. These are the positive things that we need to take home."
Spanish right-back Coke made his long-awaited Schalke debut after sustaining knee ligament damage during pre-season and the former Sevilla man enjoyed the experience.
"It was very good, it was very important for us and the fans," said Coke, who was substituted as he understandably flagged with 20 minutes remaining.
"It was a really great atmosphere. You can feel it in the stadium.
"We wanted the three points but we fought for this one point. We have to continue fighting to improve in the table."