I don't think the "you were an accident" thing is really an issue, at least not from what I see. It's the "You were an accident and we didn't want you" that is really troubling.
Seriously, I have a friend who was an accident to her parents. I found this out one night while sleeping over (I was like...13...and still had slumber parties) and her mom, for some reason, mentioned that. And then, many years down the road after she moved out of state and began having parent issues, my friend says that her mom told her she was a mistake and they didn't want her. Basically, they wish she hadn't been born, but they were God-fearing Christians who felt abortion for any reason is wrong, so they kept the baby.
Personally, if I felt like that, I would give the baby up. Much better to be in a home that loves you and wants you than one who has parents willing to tell you they don't want you.
(A year or two later, things escalated and my friend left)
But as for "oops, you were an accident" alone...I don't think it should be that big of a deal really, though if I were a parent, I might temper it with "but it was a good one," or something like that. And if it wasn't, I wouldn't have the kid anymore.