Actually this is pretty nicely described in the film's official novelisation;
When the Kelvin is initially attacked by the Narada, the high-speed missiles take them completely by surprise. Not only do they only have precious few seconds to react, but the missiles then split unexpectedly and then travel straight through their shields, courtesy of borg-tech:
“Evasive pattern delta five. Return fire, full spread! Prepare to—!”
There was no time to prepare. Unexpectedly, the incoming weapon seemed
to shatter. Instead of a single missile it devolved into a spray of
smaller yet still immensely powerful projectiles. Slamming into the
Kelvin, the unknown weapons ripped open several decks before finally
concluding their path of destruction near the main engine room.
The second time around though, they're ready for them and begins targeting the launchers themselves and anything that comes out of them:
“If we’re going down, maybe we can take these bastards with us.” He
leaned slightly forward. “Mister Pitts, set autopilot. Plot a
two-minute intercept course. We know where they’ve been firing from.
Target those weapons systems and let’s see if we can buy the shuttles