I think (a) is correct. But, how about (b), (c) , (d)?

(a) John felt pity for the old man sitting under the tree.

(b) John felt the old man was very pity / pitiful.

(c) John was pity for the old man.

(d) John was sad for the pitiful old man.
You're right, (a) is correct and the best of the four.
(b) 'pitiful' would work, but I would prefer 'thought' over 'felt'
(c) wrong
(d) 'felt' works better here
A small further comment.

'Pity' is a strong emotion.

We much more often say "I felt sorry for him'.