A lesson from my father - a professional photographer for 40 years-- that I try to remember when framing up a subject is this: What is the story of the photo? If the story is the flower, then you need it to take up the majority of the frame. Get right in there, as tight as your lens will focus, and let depth-of-field blur out the background. If it's a grouping, then do what you an to isolate the subject from what you don't care about. If you care about too much then yes, it's going to look like you just shot the first thing out of the door.
My problem is that I ignore distracting elements when I'm shooting, but the camera won't, and you'll see what you missed after the fact. In this shot, I was concentrating on the timing (it was windy that day), and didn't notice the darker flower head in the background. Happily, you can take as many practice shots as you like.
Sorry termina3, I didn't see your DOF comments bfore posting.