Actually it can mean both. If you said “je devais assister à beaucoup de réunions”, only context would make it possible to tell which meaning was intended. Usually it tends to mean “supposed to” because, quite simply, when the meaning “used to need to” is intended, a different expressions is used:

J’étais obligé d’assister à beaucoup de réunions. “I used to need to sit through a lot of meetings.”
J’étais obligé de venir chez toi. “I used to need to come to your home”