He comments on his face as if it's the first time he's seen it. I don't see how that could be taken as anything other than confirmation that he'd recently regenerated.
What, you've never commented on your appearance in the mirror after getting a hair cut or losing weight? Or checked out yourself in the mirror after meeting someone cute?
In short, there are lots of reasons why the Doctor would remark upon his appearance in the mirror that have nothing to do with regeneration.