Celtic were the better team from start to finish, and did not have any problem in winning the tie and progressing to the next round of the competition.
Burke, signed on loan from West Brom in the Championship in England in the January transfer window, started the tie and played for 67 minutes.
The former Nottingham Forest winger set up two of Scott Sinclair’s goals, and Celtic manager Rodgers was impressed.
Rodgers told BBC Sport about Burke: "He’s got huge potential, his running ability, his touch, he’s just getting back to playing football regularly again.
“His run for Scotty’s second is frightening really, that pace - at any level of the game takes people out of it.
“His square ball for it was sublime. His all-round game, he’s getting better, improving.”
Burke struggled to make an impact at West Brom, but his loan spell at Celtic is going well at the moment.
According to WhoScored, the 21-year-old has made four starts and three substitute appearances in the Scottish Premiership for the Hoops so far this season, scoring three goals in the process.