If "exclaim" means to shout out loud:
* Whisper
* Murmur
* Speak softly
* Say quietly
If "exclaim" means to express strong emotion:
* Remain silent
* Suppress emotion
* Be indifferent
* Show no reaction
If "exclaim" means to say something emphatically:
* State calmly
* Speak neutrally
* Say something matter-of-factly
Ultimately, the best opposite for "exclaim" depends on the specific situation and the intended meaning.