Incorrect.
"Exclaim" is correct. "Members" is plural and, to agree with a
plural noun, a regular, present-tense verb usually ends in -s or
-es. You may have been fooled by the words coming in between the
noun and its verb. Remember, words that come between the noun and
its verb (in this case, "of the office staff") are not words that
the verb has to agree with.
Each time I microwave a stuffed pepper for lunch, members of the office staff
exclaim, "Can we
have some, too?"