Furman picked up a fifth cap for the country of his birth in Wednesday's 1-0 defeat to Zambia, but accepts international duties have compromised his role at Boundary Park.
In his absence Robbie Simpson and James Wesolowski have forged a promising central midfield partnership, often consigning Furman to the bench, and on his latest return to the starting line-up against Tranmere last weekend, he collected a fifth booking this season to be sidelined once again for Saturday's trip to Bournemouth.
"It is difficult missing games because Oldham is my bread and butter," Furman told BBC Radio Manchester.
"I've been here for a long time and I want to see the club do well. It's tough to go away, but when your country calls, it's hard to turn down.
"It's a very difficult situation and one that I never thought I would be in. I have to go and serve my country."