If there's anyone who has a right to be furious, it's the Afghans, since the main accusations against the five (or some of the five, rather) are that they bore responsibility for massacres perpetrated against Afghans prior to or during 2001. I'm not sure just how furious they actually are, though; for at least one of the five, Karzai has been calling for his release for years. And the Afghan press seems to have mixed reactions. If the Afghan government really was sidelined and they're not just saying that, they have every reason to be ticked off, but I'm not sure where all this American fury about the exchange is coming from.

The reaction of the soldiers in his platoon is a different story, of course, I certainly understand their resentment about him being welcomed as a hero if he was really a deserter who put their lives at risks during the searches for him. But that isn't really a sufficient reason for the government to not negotiate for his release.

Edit: I should add that I don't disagree with RT that this wasn't exactly good negotiating, giving up five high-profile leaders of the enemy in return for one insignificant soldier who was a deserter at that. I have no problem with the five being released, as such, but I do think a more substantial quid pro quo could and probably should have been obtained for that. But, again, it's mainly the Afghans who are affected by that, since the Americans are basically out of Afghanistan now anyway. And definitely will be by the time Qatar lets the five return home.