Correct. The missile didn't even detonate! The impact started fires that the crew was unable to control (the impact destroyed fire suppression infrastructure) and the ship eventually sank due to fire damage.
Recent re-analysis has concluded that the Exocet actually *did* detonate and performed as advertised.
Of the two missiles that hit the USS Stark, one exploded and one did not. The Exocet that exploded actually caused minor damage, but the Exocet that did not, simply caused fires with the fuel the missile still had on board, causing much more damage. The Exocet missile had a reputation for not detonating, but causing more damage in not working properly than when it did.