Irish champions Drogheda won the game at their United Park stadium 1-0 through Aiden O'Keefe's second-half strike.
Two former Shamrock Rovers players were included in Gannon's starting line-up. Dane Massey, 19, who has already spent a trial period at Edgeley Park played at left-back with 20-year-old Stephen Nolan leading the attack.
And in the second-half, Paddy Madden, a 17-year-old from Irish junior club WFTA, came on as a substitute.
Gannon's side was otherwise made up of players who weren't involved in Saturday's victory at Hereford, in a game which made it seven straight wins on the road for County.
The first-teamers were encouraged to use the trip to Dublin as a chance to relax before the rigors of the final 12 games of the season.
Midfielder Gary Dicker, who arrived at Edgeley Park from University College Dublin last summer, was particularly pleased with the choice of Ireland for the mid-season break.
"It's great to be home for a few days and it's great that we came to Dublin," he said.
"I've nipped home to see the family, so it's a good trip for me and the other Irish lads, Leon McSweeney and Conrad Logan.
"It's just been great to relax for a few days and just chill out
"We've had a lot of games on Saturdays and Tuesdays so it's good to get a rest."
But Dicker's mind is firmly on the promotion race, believing that County can still aim higher than the play-off place they currently occupy.
Bradford City and Rochdale visit Edgeley Park on Saturday and Tuesday respectively and Dicker sees those games as a chance for County to start replicating their tremendous away record at home.
"We just have to start picking up the points at home," he said.
"Hopefully, Saturday will kick-start that.
"We've got a game in hand on the two teams ahead of us so we want to get into that fifth place as soon as possible.
"Then, hopefully, we can push on and get in to the automatic promotion places." Tweet

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According to the Shamrock Rovers site young Dane Massey could open a tin can with his left foot its so good, If Jim is using his Irish contacts to get first pick of these kids it looks like county have unearthed a gold mine.At least they will feel at home at Edgeley Park with so many Irish connections already there.
The lads were not former Shamrock Rovers players they are both a vital part of their u21 team for the coming season, unless county sign them