So the question becomes: how is the battery secured inside the MacBook? You didn’t specify which MackBook model you have... and there were different mechanisms for securing/retaining the battery in place. Lacking the pull tab, is it possible that the battery is glued in (doubtful, but possible)? Or are there retaining clips/screws holding it in place? Have you tried GENTLY prying it up with a spudger?
Not really sure how to help or what to suggest... except to start with precisely which MacBook model is it?