Gotti insulted and criticized each person including his his most trusted men, like Sammy Gravano.
The one he was afraid was Chin Gigante, both because Chin was the boss of the Genovese and because Gotti knew that even if he wanted to take revenge for the death of DeCicco, knew he couldn't declare war to the Genovese.
If he did, the other families in the best case, would remain neutral, at worst they would jump on the Gambino, Gotti before if he won't been killed by his men also were the 80s not in the mafia golden age and the gambino would have gone the end of the colombo after the war of the 90s.