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.
Stalybridge went ahead when winger Neil Kengni swivelled in the box to fire home after the Clarets couldn’t clear a corner in a disappointing start.
And the visitors were undone again just two minutes later when experienced striker Craig Hobson headed home.
The former Stockport County frontman proved a real handful for the Clarets’ central defensive pairing of Ollie Younger and ex-Celtic loanee Scott Wilson.
The pair gradually got to grips with the challenge as Burnley often tried to play their way out from the back - not always with great success.
But it was a superb piece of football that saw Stone’s side briefly get back in the contest.
A brilliant through-ball from a midfield trialist dissected the Celtic defence and found Bayode, whose quick feet saw the winger round goalkeeper Patrick Mahome and slot home.
Mahome had earlier saved a thumping volley from Chris Conn-Clarke and a second trialist should have levelled with a chance he clipped wide.
But just when it looked as though the Clarets might build up a head of steam they conceded a poor third goal.
Kengni’s low cross should have been dealt with by goalkeeper Kai Calderbank-Park but he was beaten at the near post, possibly via a touch from Hobson.
The Clarets recovered from that set-back to dominate possession after the break – switching to a 4-3-3 formation when the injured Bayode was replaced by Will Harris.
But despite the efforts of Rob Harker to lead from the front they failed to create any real opportunities to get back into contention.
It was Celtic who went closest a couple of times to adding to their score through a trialist and Craig Valentine before Younger headed wide from a late corner from the Clarets’ last opening of a disappointing night.
Stalybridge Celtic: Mahome; Walker, Darnold, Allen (Dalton HT), O’Halloran; Stafford (Bortles HT), Rosen, Dent Lees HT), Kengni (Ryan 67); Hobson (Carr 67), Valentine. Substitutes: Lees, Bortles, Dalton, Ryan, Carr.
Burnley: Calderbank-Park; Cropper, Younger, Wilson, Glennon; Bayode (Harris 62), Trialist, N’Guessan, Conn-Clarke; Trialist, Harker. Substitutes: Allen, Pruti, Cooney, Thomas, Steels, Senior.