Martinez claims that Kone, 29, has been put in an impossible situation after winning back his international place since moving to the DW Stadium from Spain in the summer.
"At the moment Arouna will join up with the Ivory Coast," said Martinez. "He hasn't got much choice because, as a player, if you decide not to go that's calling it a day to represent your country.
"I had a chat with Arouna and he wants to stay. But in the same manner he doesn't want to let his country down and that's understandable. It's so wrong for the players to have to miss one or the other.
"It's very unfair. I don't think this event should be held while the Premier League is being played. There must be ways to make sure the players don't have to be in this position."
Asked if Kone's teammates might be able to sway his decision, Martinez joked: "The Christmas party could have a big say in it!"