The whole point of the Enterprise-D was that it was so advanced that it could virtually fly itself, or with minimal crew input. The bridge was deliberately minimalist for this reason.
Indeed it practically does fly itself in a few episodes - 11001001, Brothers, Remember Me (sort of). Starfleet ships in Redemption had small crews. Voyager was operated by one medical hologram or ex-Borg on a few occasions. The Prometheus won a battle against a bunch of Romulan warbirds entirely under computer control.
They don't need hundreds of cartographers, medical staff, security officers, botanists, teachers, barbers etc, which is what most of the crew was.
They could probably do with some engineering staff, and if they take severe damage things could go south quickly, but presumably Geordi has some drones to take care of the essentials.
Obviously it's not going to be operating at peak efficiency, but it's a desperate situation and running that ship with a minimal crew is entirely consistent with TNG.