The United States international, who celebrated his 24th birthday on Wednesday, had a hand in both his side's goals as the Barclays Premier League strugglers saw off a much-changed Southampton 2-1 at the Stadium of Light.
Their reward is a last-eight clash with Poyet's former club Chelsea on Wearside on December 17, but the Uruguayan is hoping for more of the same from the £6million man, who has scored just once for the club, during the intervening weeks after he set up first Phil Bardsley and then substitute Sebastian Larsson.
Poyet said: "He was a big part of the first goal - it was a great header, headed down, headed properly, strongly. He was in the right place, the goalkeeper made a save.
"The second one, which is the key goal of the game, another striker would think about himself and have a shot for himself.
"He thought about the team, so you have to give him credit. He allowed Seb Larsson to score and there are not many people of that calibre in his situation - I know plenty and I played with plenty of strikers who in that situation would have had a shot.
"They don't care about anything but themselves, so I am very pleased for him. We need to be really happy with what he did for us.
"The more he contributes and the more we play, I will tell you the more chances he will get. Today was probably the first clear chance he has had, the header."
After a rather uneventful first half, Sunderland took the lead with 59 minutes gone when Altidore powered in a header which keeper Kelvin Davis could only parry and Bardsley pounced from close range.
The American's astute pass allowed Larsson to extend the lead with four minutes remaining and although Maya Yoshida reduced the deficit as time ran down, there was no way back for the visitors.
Southampton assistant manager Jesus Perez said: "We are a little bit disappointed to be out of the cup because it was an important competition for us to provide minutes for our squad and for our youngsters who, as you know, we like to use.
"But in the end with the result, we could change nothing. Obviously, we think we deserve more - there were special situations that we could have managed.
"But we have to say well done to Sunderland. They tried to win the game and they deserve, obviously, to be still in this competition."
It was just Sunderland's fourth win of a troubled season, and Poyet's optimism was increased by an impressive performance by defender Wes Brown in his fist competitive start since January last year.
He said: "When you have played in the Premier League for a team like Manchester United, it's always important to have him in there.
"He reads the game well, he has experience. That class of player can give you something that others can't."