The Italy international was part of former boss Paolo Di Canio's close-season recruitment, signing a four-year deal after moving from Serie A champions Juventus.
Giaccherini has started seven games for Sunderland in the Premier League this season, but was omitted from the starting line-up as the team picked up their first league triumph of the season in a 2-1 win over rivals Newcastle United on Sunday.
Inter are reportedly interested in taking the 28-year-old back to Italy, but Poyet envisages Giaccherini will have a big role at the Stadium of Light this season.
"He is frustrated, he is not happy, but he is a very good professional," he said.
"It's difficult for him to take being out of the team, but I'm expecting Giacci (Giaccherini) 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."
Poyet refused to be drawn on Inter's links to the midfielder, but admitted he will discuss the futures of several members of his squad during the upcoming international break.
He added: "We will wait for them (Inter). 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."
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