He couldn't remember me
Er konnte sich mich nicht erinnern
is that right ?
No.
"to remember" in English is a transitive verb. You use it this way:
Somebody remembers something.
In this pattern "somebody" is a person. This person is performing an action with a thing, that is not the person itself. The thing, that is taken form your minds dark basement out to the bright light of awareness is a memory. The "something" in the pattern is such a memory.
German works different, because the verb "erinnern" is not transitive. It is reflexive.
Jemand erinnert sich an etwas.
In the German pattern "jemand" is the same person as "somebody" in the english pattern. And again, this person is doing something, but not with something else! The person is doing something with himself/herself. In German you can't remember a memory. In German you always remember yourself! This is a big difference!
What the memory is, that is brought to the light of awareness, must be told in a separate part of speech: »an etwas«.
The word »an« is a preposition, and after this preposition comes an object in accusative case. And this object is the memory. But this object is optional. You don't need to tell it in German.
The German word "erinnern" has second translation in English. It can be "remember", but also "remind". But when you use it in this meaning, "erinnern" is no longer reflexiv:
Chris erinnert sich an das Treffen.
Chris remembers the meeting.Chris erinnert mich an das Treffen.
Chris reminds me of the meeting.
sich an etwas erinnern to remember something
Er konnte sich nicht an mich erinnern.
This can also be used with the genitive:
Er konnte sich meiner nicht erinnern.
etwas erinnern to remember something, heard rarely
Er konnte mich nicht erinnern.
jemanden an etwas erinnern to remind someone of something
This one can sometimes be confused with the other versions.
Sie erinnert ihn an seinen Termin, indem sie ihn anruft.
Sie erinnert ihn an seine Mutter, die genauso lebensfroh war.
Ich erinnere mich daran, den Müll rauszubringen. (Because I see the trash, or because I made a note about it.)