Just as a photon torpedo is able to maintain warp flight using a warp sustainer engine (even though it has no warp core itself), so too should a ship be able to sustain a warp field on auxiliary power for some time after a warp core is no longer present/active. Here is the relevant excerpt from the photon torpedo entry on Memory Alpha, taken from the Star Trek: The Next Generation Technical Manual:
The propulsion system of the torpedoes is a warp sustainer engine. The
engine coils of the torpedo grab and hold a hand-off field from the
launcher tube's sequential field induction coils. A miniature
matter/antimatter fuel cell adds power to the hand-off field. When
launched in warp flight, torpedo will continue to travel at warp, when
launched at sublight, torpedo will travel at a high sublight speed,
but will not cross the warp threshold. (pg. 129)
As Kalamane points out in a comment, the ability to maintain a warp field without a warp core has been referenced before in the TNG episode "Brothers". The excerpt from the script:
PICARD: Mister La Forge, prepare for saucer separation.
WESLEY: Sir, we're at Warp nine three.
PICARD: I am aware of the risks, Ensign. When the umbilical splits, we should regain primary control, do you agree?
LAFORGE: Yes, sir.
PICARD: The saucer module should fall out of warp in two minutes. Be prepared to sweep back. Pull it in with a tractor beam.
If the warp-core-less saucer section has enough power to maintain a hand-off warp field from the secondary hull for a couple of minutes, then a whole ship that has lost its warp core should be able to do the same.