Well, as you can plainly see, opinions vary. It depends on the goals you have set for yourself. If you are going to be a competitive archer, no, that is probably not acceptable. If you are trying to kill a deer, I would say yes, and this is why.
You don't have to hit a deer in the heart to kill him cleanly. A double lung shot will do it efficiently. The heart of a deer iswhat, approximately 3"? The kill zone on a deer, the lungs, aka, boiler room, are roughly 7".
As I said, unless you are a target shooter, I don't think groups matter as much. There is only one shot that counts.....the first one. That's all you are going to get at a deer anyway. Groups indicate consistency, or lack thereof. If you can put your first shot in a 3" circle, every time you go out and shoot, you will kill your deer.
There are just too many variables IMO that affect groups. Arrow quality, bow quality, release quality, just to name a few. If you shoot 3" groups, that sounds pretty consistent to me.
Some people are just harder on themselves than others, and demand more of themselves. Nothing wrong with that. Set your personal goals and achieve them.