On the 737NG.
Windshear is a function of the GPWS. Predicitive windshear is a radar function.
To answer your question: FOM Vol. 2. Section 15 "Warning Systems" says that "The GPWS provides a warning when the aeroplane is in windshear".
It goes on to say you will get the two tone siren followed by "WINDSHEAR", the red "WINDSHEAR" on both attitude indicators, and this is caused by "excessive" windshear in the current aeroplane position detected by the GPWS, and that it is enabled below 1500' RA. GPWS windshear detection begins at rotation.
In your case you were either too high (>1500'RA) or the machine decided you were not in windshear!
Hope that helps.