Dortmund travelled to Stamford Bridge for Tuesday's second leg holding a 1-0 advantage on aggregate, and they had moments in the first half to extend that lead.
However, Chelsea eventually turned the tie around courtesy of goals from Raheem Sterling and Kai Havertz either side of half time as they booked their spot in the quarter-finals.
Home supporters grew frustrated in the first half with Dortmund being awarded what could be perceived to be a number of soft free kicks, while a shove on Havertz inside the penalty area when he was about to shoot went unpunished.
In the second half, though, there were talking points over Havertz's conversion from the penalty spot at the second time of asking.
Marius Wolf was initially adjudged to have handled the ball after an attempted Ben Chilwell cross struck his arm from close range, the decision being given after referee Danny Makkelie was advised to go to the pitchside monitor.
Havertz proceed to miss the subsequent spot kick, only to be handed a reprieve when his shot hit the post and was cleared by Salih Ozcan who had been present in the 'D', deemed to be encroachment.
After Havertz scored the retake, Chelsea battled their way over line, but Can's focus was on the referee when addressing the media after the match.
As quoted by the Daily Mail, Can said: "The referee. It was his fault today. How can you give the second penalty in the situation? How does it work? That simply does not work!
"I don't give a s*** who walked in there before. He was arrogant the whole game - that's where it starts. We lost here undeservedly because of the referee.
"We play here at Stamford Bridge. Maybe he's afraid of the fans, I don't know, but then UEFA should send another referee."
Defeat for Dortmund brought their 10-match winning streak in all competitions to an end ahead of their trip to Schalke 04 on Saturday.