Neutrinos are certainly affected by gravity. However extreme gravity may be around the collapsing core of a massive star, the real problem is great density of matter. Neutrinos interact with the stellar matter much less than other particles so they escape much easier, though the very center of the collapsing core is opaque even to them.

In fact, the main problem of the supernova-to-be massive star is not where to get energy (it is at hand in the form of potential gravitational energy) but how to get rid of it! Energy must be carried away from the core to enable collapse - and it is carried away by the neutrinos.

However, even neutrinos don't escape from the collapsing star instantaneously. About 1 per cent of their energy is absorbed in outer layers, reversing their collapse to explosion.

Neutrinos are certainly affected by gravity. However extreme gravity may be around the collapsing core of a massive star, the real problem is great density of matter. Neutrinos interact with the stellar matter much less than other particles so they escape much easier, though the very center of the collapsing core is opaque even to them.

In fact, the main problem of the supernova-to-be massive star is not where to get energy (it is at hand in the form of potential gravitational energy) but how to get rid of it! Energy must be carried away from the core to enable collapse - and it is carried away by the neutrinos.

However, even neutrinos don't escape from the collapsing star instantaneously. About 1 per cent of their energy is absorbed in outer layers, reversing their collapse to explosion - the visible firework of the supernova. The rest (99 per cent !) of the original gravitational energy is quietly carried away by neutrinos.