It was certainly a contributing factor. I suggest reading One Minute to Midnight, by Dobbs.

Khrushchev's memoirs support the assertion that the Bay of Pigs invasion, though it failed, inspired fears that the United States would keep trying to overthrow Castro. "One thought kept hammering away at my brain: What will happen if we lose Cuba? It would have been a terrible blow to Marxism-Leninism."

Supplying nuclear missiles, Khrushchev thought, would make Cuba invulnerable to invasion and equalize the balance of power. Khrushchev knew the missile gap did not favor his country, and he believed installing missiles in Cuba was a win-win.

For his part, Castro thought along similar lines. His writings show that he viewed the Bay of Pigs as a turning point, that no compromise with the United States was possible, and confrontation was the best possible option to ensure Cuba's security.