Asking my Professor to create a Google Account to submit a Letter of Recommendation for me
My best guess, and just a guess, is that he was frustrated with the system that was required, rather than with you. It is probably a mistake for any admissions system to require an email address from a particular provider (unless it was for a job at Google, I suppose). 

I don't think you made an error, but if you want to ease the waters, go see him and apologize for the hassle of it all. It would probably be a mistake to just forget about it, but also a mistake to obsess over it. 

Such systems infuriate me, also. Such extra accounts are always a security/privacy issue.