The former Manchester United player has been plagued by a number of injury woes following a knee problem that he picked up in January last year.
"I respect the medical staff, and when I got here, we had everyone fit which was impressive," Poyet told the Shields Gazette. "I said to them that I'll follow them. If they tell me that Wes needs a rest, then I'll go with them.
"But we talk to the player, and he has a big input into that as well. Whether it's Wes, [Steven] Fletcher or Phil [Bardsley], who have been the ones who've had the problems, it's important to have that communication with them."
After three weeks of full training, Brown competed in two-and-a-half fixtures last week.