If you recheck the movie, you will notice that when Kirk opened fire on the Narada, the Enterprise was extremely close to it.
Instead of pulling his ship away to maximum distance and THEN firing on Nero, Kirk instead fired from a proverbial spitting distance.
That's basically how the Enterprise got trapped by the gravitational field of the black hole.
In TNG and VOY, areas of space with sufficiently strong gravitational fields (black holes included) did interfere with Warp drive.
Subspace fields can be collapsed under such circumstances, and since Starfleet ships utilize subspace fields around them to not just lower their mass, but also to formulate Warp bubbles (and likely other normal operations), it is quite likely that being so close to the singularity would destabilize the Warp field.
Mind you, we also saw that ships can get away from black holes (as sublight) with a little ingenuity, and subspace fields COULD be established under extreme circumstances if you can provide the needed energy, or modulate them so they could work there. Often times, modulating the existing subspace fields and adapting them to the situation works better than just pumping more power into them does.
In Voyager 'Hunters' episode, when the ship approached the Hirogen communication station, the station was emitting strong gravitational fields from 2 Ly's away.
Voyager even weakened the station's containment field to use the gravitational eddies against the Hirogen.
Prior to doing this, Janewas asked Kim to do the following:
JANEWAY: Don't worry, we're going to be ready for it. Harry, create a low level warp field around Voyager. Sublight energy level. That should help counteract the gravitational pull.
So, gravitational pulls CAN be counteracted using subspace field emissions... but Voyager was also more than a century ahead of the Enterprise in 2009, and when the ship was caught in the gravitational pull because the Hirogen wouldn't stop firing, this is how Voyager escaped:
JANEWAY: Open the antimatter injectors to one hundred twenty percent.
KIM: Captain, that could breach the core.
JANEWAY: So will that black hole. Now just do it.
Voyager took place over 100 years after 2009... and it is possible that doing the same thing on the Enterprise would not have been successful (its supposed to be a much less powerful ship, so it simply might not have had enough energy to do that).
Opening the antimatter injectors to 120% on Voyager to escape the Black hole could be equivalent to detonating over a century older Enterprise's warp cores and ride the shockwaves out (Voyager rode the shockwaves too in various situations).