Will I get a negative LOR from my professor
I don't think that there should be any issue. Your professor is right - most LORs are submitted directly by the referee to the university (to avoid the risk of falsified references). I would thank the professor again, say something like "yes, I thought that it's kinda weird that the system asked me to submit the reference. It makes much more sense that you do it" (putting you and the professor on the same page, while placing the blame on the system rather than on yourself). 

Generally speaking, it would be good to have a few referees to rely on, but I don't think that this incident "burned" one of your referees.

Good luck!