With the game tied at 1-1 with 17 minutes remaining, referee Szymon Marciniak awarded a penalty to Portugal for a handball but changed his mind after speaking to his assistant.
Portugal had chances to take the lead before the final whistle, with full-back Raphael Guerreiro, Bernardo Silva and Pepe all seeing shots miss the target deep in stoppage time.
While Cancelo believes his side were on top throughout, he says the referee played a decisive role in the match, saying UEFA should have allowed video technology in the preliminary rounds.
"The referee has affected the outcome of the game," the 24-year-old told RTP. "With the technology that we have today, I believe it is the referee's and UEFA's incompetence not to have VAR in the qualifying stage for the European Championship.
"Of course we all made individual mistakes, but I think we were clearly superior. Serbia just stayed back."
The result leaves Portugal on two points from as many games in Euro 2020 qualifying, having already drawn with Group B leaders Ukraine on Friday.
Cancelo is not worried about their start, however, as they have plenty of time to recover.
"There is a lot to play for," the Juventus full-back added. "Ukraine and Serbia are big teams but I think Portugal have the quality to win in both Ukraine and Serbia."
After the conclusion of their UEFA Nations League campaign in June, Portugal resume Euro 2020 qualifying with a trips to Serbia and Lithuania in September.