Could Karpov defend against Kasparov in 1990 championship? I have watched this video, where Kasparov explains the variations after his knight sacrifice. However, the position he analyses starting from 3:08, I think I am missing something.

Kasparov vs Karpov, 1990 World Finals

[FEN "r3qb1k/1b4p1/p2pr2p/3n4/Pnp1N1N1/6RP/1B3PP1/1B1QR1K1 w - - 0 1"]

1. Nxh6 Rxh6 2. Nxd6 Qxe1+ 3. Qxe1 Rxd6 4. Qe4 Nd3


What if black plays 

[FEN "r4b1k/1b4p1/p2r4/3n4/Pnp1Q3/6RP/1B3PP1/1B4K1 b - - 0 1"]

1... Nf6


instead of Nd3? Can't he both attack queen and defend h7 square? His chances of survival is so low, obviously, but I think Nf6 is better than Nd3, and worth analyzing.
Nf6 is followed by e.g.:

[FEN "r4b1k/1b4p1/p2r1n2/8/Pnp1Q3/6RP/1B3PP1/1B4K1 w - - 0 1"]

1. Qh4+ Kg8 2. Bxf6 Rxf6 3. Qxf6


with not only huge material advantage for white, but also some very nasty threats that are ultimately not defendable. So in short, there is not much to gain with Nf6.