No, you should not. However, it depends on what you consider supporting the troops. Many consider it throwing a yellow ribbon on their bumper and forgetting about us. Many consider it to be the gov't continually voting to bloat the DOD's budget to astronomical levels. Many consider it to be mailing cookies and care packages to us in country <-awesome. However, if you really want to support us, stop voting war mongers into office. Stop voting guys in that will send us off as political fodder to a some third world trash can to "nation build".
Do we fight in unjust wars? Yeah, we are now. Not my fault either. If you want a military that can pick and choose what wars it fights, then you'll have anarchy. We can't pick and choose the venue and cause for the wars we fight. It's not civilized. However, we can depend upon the people who "support" us to recognize the unjust war and stop voting for the people who send us to them.
Do we massacre people? No, it has not happened in these wars minus the one wierdo who recently killed a bunch of Afghanis. If it did, no, you shouldn't support it.
The bigger point to make is instead of pointing the finger at us for starting to get a little sloppy in the PR campaign aka Operation Enduring and the recently ended Iraqi Freedom, how about looking in the mirror. Who have you voted for? What have you done to prevent me from being there to begin with? If you voted Pres W Bush, you voted for war in 2004. If you voted Pres Obama in 2012, you voted war as well. If you voted McCain or Romney, you voted war. So instead of saying "Hey, don't pee on that corpse!" you should say to yourself "Hey, don't vote for that neo-con/lib!"
If any of the above isn't a big voting issue for you, that's fine. This is America after all. You can vote for what you want. However, if this isn't a voting issue for you, it shouldn't be a debating issue either. You're a part of the problem and a hypocrite IMO.