The Black Cats' new boss Gus Poyet enjoyed a 2-1 success over arch-rivals Newcastle at the Stadium of Light.
But the USA international has pleaded with his team-mates to show the same kind of passion against his former club at the KC Stadium this weekend.
"It is a winnable game (at Hull) and we have to make sure we go there and show the same effort as we did on Sunday," admitted the 23-year-old striker.
"It is huge. It is important now to kick on and keep going, not just be satisfied."
Altidore also admitted he is hopeful of striking up a regular partnership with Steven Fletcher in attack after the Scotland forward's early season was hampered by injury.
"It has been difficult for him because he has been out injured a lot and he was only training a little bit until recently," he said.
"It has been great to have him out training again and when he is on the field in match situations it gives everybody else room to operate and be more dangerous.
"We have worked on set-pieces quite a bit so it was nice to see one work out with Fletch scoring.
"We just need to get him healthy and keep him that way."