Burke claimed a goal and an assist as Forest's development side overcame the Tykes 3-2, and Gilligan was impressed by the wide-man.
He says that Burke showed composure in front of goal and important creativity during the fixture, as the 18-year-old helped his side claim an impressive three points.
“He took his first goal brilliantly. To run from five or ten yards inside his own half, take the ball and pop it past the goalkeeper was fantastic," Gilligan said.
“And for his cross, when he’s running off the pitch, to get his foot around the ball and put it in for Matty Cash to score at the near post was exciting as well.”
Could Burke see more senior minutes this season?
With Burke impressing for the under-21 side, it would come as no surprise were Dougie Freedman to draft into him into the senior squad for the remaining two games of the Championship season.
The Reds have little left to play for and it may be of benefit to all concerned if the Scottish manager gives some of the side's leading prospects a run out now, as he plans for the future.
Freedman is a known admirer of Burke and gave the winger his debut earlier in the season, before sending him out on loan to Bradford City.
If Burke could develop into a star for Forest it would be a major boost, as Freedman has already expressed a desire to add more wingers to his squad.