Hello V... O...: Well... I don't know... from what you wrote it sounds to me as though your gesture was sincere & appropriate. I'm not sure what more one could do.

Yes, you forgot your friend's birthday. These things happen. The important thing here, at least from my perspective, is that you made a sincere effort to acknowledge your oversight & to make an apologetic gesture. From where I sit, this is to be celebrated!
I personally don't celebrate, or even acknowledge, my birthday. (You won't see my birthdate listed on my profile page.)

There was a nonsectarian Indian mystic named Ramana Maharshi who supposedly said: "Celebrating birthdays is like throwing flowers on a corpse."

I know birthdays are important to most people. But with regard to my own, that is the perspective I maintain.
I think that impulsivity & "reservedness" are sort-of the two ends of a continuum. I know in my own case I'm pretty far over toward the "reservedness" end at this point in my life. Perhaps it's my age. It hasn't always been that way. Over the years, I've done some breathtakingly impulsive things.

It often didn't work out well.

I think a large part of what life ends up being about is trying to find & maintain oneself more-or-less around the center of the impulsivity / "reservedness" continuum. It's what the Buddha called the middle way...