However, they might not be allowed to voice their objections. After all, Klingons were good guys and Cardassians were bad guys in the war, from the point of view of those who won - so it would not be possible for the losers to complain about their losses, any more than it was possible for the Germans or the Japanese to mourn their losses after WWII.
It's not known whether the Cardassians inflicted major casualties on the Federation as such in the war; probably not. Nevertheless, if postwar Cardassia complained of something the Klingons did, the likely reaction of the Federation would be to say "you only got what you deserved", as there would be major UFP displeasure over the fact that Cardassian actions had made the war possible in the first place.
Dukat's unilateral actions made the war possible. We do not even know what percentage of the Cardassian people, if we could somehow get a poll where everybody would feel comfortable reporting their honest opinions, would have backed that alliance.
And who says the Germans and Japanese had no right to mourn the people that the monstrous dictators in charge of their country drafted as cannon fodder? Not every person wearing an enemy uniform was necessarily sympathetic to that political platform--though of course a good number were.
At least in modern society, nations have been called to account for their soldiers' actions even in wars where they were the victors. Had people taken the attitude you describe of "tough, you brought it on yourselves," I don't think we would've had the controversies over Guantanamo Bay, Abu Ghraib, or Haditha (the latter being an action where civilians were killed, the former two involving actual enemy combatants)--or perhaps most aptly, controversy over whether the bomb should've been dropped on Hiroshima and Nagasaki. Given this, I would say there is at least precedent for such a complaint to be considered.