The youngster, who is 16 years, nine months and 21 days old, became the youngest ever Celtic player to feature in European competition, and the youngest ever to play for a Scottish team in Europe.
Dembele came on as a 72nd-minute replacement for Mikey Johnston, but was unable to help the Hoops maintain their unbeaten record during the group stage of this year's competition.
Goals from Burca and Djokovic ensured Cluj join Celtic in the knock-out stages, with the draw for the next round to be made on Monday December 16.
Dembele made his competitive Celtic debut as a second-half substitute last season, in a 2-1 win over Hearts at Celtic Park on the final day of the league season.
The London-born player has represented both England and Scotland at Under-16 and Under-17 level, but has pledged his allegiance to the country of his birth.