Electronics Repair Questions? Ask an Electronics Technician
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If there is a chirping coming from the ceiling... or seems to be... try using a stethescope, or a home-made equivalent made of a rolled-up sheet of paper or paper cone, and try listening as to whether the chirping is coming from the ceiling or from the alarm on the table.
The 'mount' piece of the smoke alarm may still have the 'sound' or 'speaker' portion of the smoke alarm on it, if the chirping is indeed still coming from the ceiling. If so, you didn't remove the alarm proper, but only its outer cover.
Let me know what maker and model of alarm you have, please. And I will advise you further.