Altidore, who endured a disappointing spell on loan at Hull City four years ago, drew a blank on his debut as Sunderland went down 1-0 to Fulham at the Stadium of Light.
The 23-year-old insists he has not set himself any personal goalscoring targets, but has vowed to score goals for Paolo Di Canio's side.
"I'm confident I will score goals," Altidore said. "I don't set myself targets, but I'm expected to score goals, and that's what I will do.
"When I was last here, I was just 19 and had no experience of European football.
"But since then, I think my record speaks for itself."
Meanwhile, Di Canio believes he can bring the best out of Altidore by working closely with him.
"Jozy is good but he can improve and I can be a very good coach for him," noted Di Canio.
"We are here to improve and I'm sure the players will but they have to listen to me.
"Jozy is only 23 and is stronger than he was the last time he was in the Premier League, but he will get better.
"We are working on his movement and stretching defences, because otherwise he can become difficult."