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The Milk Cup split into three separate competitions after the first two games and the young Clarets are now competing for the Dunluce Trophy, a mini league involving three other teams.
The opposition in Coleraine, Co Fermanagh never looked like causing trouble and Burnley were unlucky not to win all three points having created all of the game's goal scoring opportunities.
Terry Pashley made four changes to the team that lost 5-3 to Trudovye Rezervy.
Forward James Taylor was given his first start while Curtis Woods returned from his one-match suspension to resume his duties at centre half.
Under-16 Kyle Reilly, who had been called into the Milk Cup squad at short notice, was also selected while Canadian trialist Jacob Matthews started in goal.
Woods' return meant Edward Williams moved to right back with captain Dom Knowles moving back into midfield.
All the early pressure came from the Clarets, with midfielders Liam Newman and David Lynch both going close.
Fermanagh goalkeeper Andrew Nevin then appeared to carry the ball outside his area while under pressure from Taylor but the linesman, who along with a group of players' parents was the best placed, waved away the appeals.
Again the danger man was Newman who had three further efforts, the third forcing Nevin to make a fine save.
Burnley's play was characterised by quick throw-ins, one-touch passing and good movement but they lacked the cutting edge needed to make a breakthrough.
Fermanagh almost caught out the Burnley defence on the stroke of halftime when Miki Haveron ran onto a long ball but had his shot well blocked by the retreating Stephen Edwards.
It was Fermanagh's best effort and in the second half they only enjoyed one more chance, almost identical to the first.
Matthews, who as the Canadians say, is undertaking an "assessment" with Burnley did not have a save to make, although he had a noticeable presence in the box, dealing comfortably with crosses.
There were some good passing exchanges between Knowles, Newman and left back Jake McEneaney but again there was no quality final pass until close to the final whistle.
A deep cross by McEneaney's found Knowles who controlled the ball well but his shot was too close to Nevin who saved meaning the game ended goalless.
The fourth game in as many days will be against Club Cantolao from Peru. A win will give the Clarets a chance of silverware.
Burnley team: Matthews, Williams, Woods, Edwards, McEneaney, Wilson, Newman, Knowles, Lynch, Reilly, Taylor