Since they have already agreed that it was an error I would ask the Prof to issue a correction adding you as an author. It's a simple enough process and how to do it is well documented by most journals. Refusing to correct the record would be a publication ethics issue.
Why do you think that doing this would make you lose standing in a Professor's eyes?
I am a research integrity lead at my institution and I would be appalled if a Prof refused to do this, or other senior staff were advising a post-doc or student not to pursue it. Rightly or wrongly publication is our currency and refusing to acknowledge junior staff contributions is extremely poor. I would almost think that issuing a correction would help the Prof to get the reputation for doing the right thing by his team.