If "shrugged" means "to express indifference or lack of knowledge":
* Acknowledged
* Responded
* Reacted
* Cared (as in "He cared about the problem")
* Paid attention
If "shrugged" means "to raise one's shoulders":
* Lowered
* Dropped
* Sunk
If "shrugged" implies a specific action like "shrugged off a coat":
* Put on
* Donned
* Adjusted
It's best to consider the context and choose the word that best expresses the opposite meaning you are trying to convey.