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 nothing to them (literally one emaila simple enough process and how to the editor) but refusingdo 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.