The Clarets conceded three first-half goals to lose their opening friendly on home soil.
Having won 2-1 against Pogon Szczecin’s youngsters in Poland on Saturday, Steve Stone’s side found this a tougher test against the BetVictor League Premier Division side.
And leaking two goals from corners inside the opening six minutes proved too great an obstacle to overcome against an older and physically stronger line-up.
Tunde Bayode reduced the arrears with a classy response with almost half an hour gone.
But another soft goal gifted to Celtic seven minutes before the break nipped a potential comeback in the bud as the Clarets were kept at arm’s length.