The 28-year old, who joined from Juventus during the summer, was the most expensive of former manager Paolo Di Canio's signings, but lost his place in the Black Cats' starting line-up for the 2-1 Wear-Tyne derby win.
Inter Milan are reported to be monitoring Giaccherini's situation at the Stadium of Light, although Poyet says that the Italy international will still feature heavily for his side this season.
"He is frustrated, he is not happy, but he is a very good professional," he told The Times.
"It's difficult for him to take being out of the team, but I'm expecting Giacci to be ready.
"He will play, a lot. I can't give him everything he wants because he wants to play every game for 90 minutes but he will play a big part for us.
"We're trying to make sure every single player who came here in the summer really adapts to the club. We have to become one football team and not 25 individuals."
Speaking of Inter's supposed interest in the winger, Poyet refused to draw upon any speculation, but he says that the forthcoming international break will see him discuss the futures of a number of his players.
"We will wait for them," he added. "We don't make any comments before it happens because there are too many rumours in football.
"During the international week I'm going to sit down with the people from the club, give my opinion on the whole squad and every single player and we'll analyse and then we're going to move forward."