The Hammers boss made seven changes for Tuesday's Carling Cup fourth-round tie but was delighted as his side ran out 2-1 winners at the Stadium of Light, their first victory over top-flight opposition to date this season.
Grant's side currently sit bottom with just one point from their five games ahead of Saturday's home clash with Tottenham, but he is confident they can get themselves out of trouble.
He said: "I am very optimistic about the future of this club. We know what we are doing, we have a vision about this club and I am optimistic about it.
"If you have seen our games, this is not the place for us, but we need to take points. We have a long, long season. I think it will be very hard, but it will be possible."
Nigerian striker Victor Obinna won the game 14 minutes after the break as the Hammers showed impressive character having had their early lead cancelled out.
Obinna had earlier played in Frederic Piquionne to round goalkeeper Simon Mignolet with 35 minutes gone.
Indeed, had it not been for the Belgian, the visitors might have been 3-0 up with 37 minutes gone as he denied Obinna, Piquionne and Scott Parker either side of the goal.
The impetus looked to have shifted when the Black Cats' record signing Asamoah Gyan headed home a 41st-minute Jordan Henderson corner.
However, it was the Londoners who snatched the win when the hugely impressive Parker twice combined with winger Pablo Barrera before the Mexican fed Obinna to fire into the bottom corner.
Grant said: "After so many games from which we took zero points and we have played well, except in the first game - we played well against Bolton, we played well against Chelsea - it is good for the players to see that if we continue to do the right things, we can get results.
"I believe in the football you saw today. It is good for the confidence of the players that they have a reward from the game.
"It's very important to us to come to a place like this and win the game because the players feel we have played well in the last games.
"But it is very frustrating when we play so well but don't take three points."
Opposite number Steve Bruce's disappointment was compounded by hamstring injuries to Gyan, Anton Ferdinand and Kieran Richardson after he opted to field a strong side ahead of Saturday's league visit to Liverpool.
He said: "We were flat from the first whistle. The one thing I did analyse was could we go again so quickly after what we did against Arsenal?
"I decided to go with mainly what we did against Arsenal, but we looked off it and it was plainly evident to see.
"I stuck with it because I thought with what happened at the weekend, we would fly into the match.
"But obviously the game against Arsenal took a lot out of us. Some of them had run the equivalent of the Great North Run and to try to do it again was difficult.
"They can do it, but not at the intensity and that showed. Maybe in hindsight I should have made more changes to freshen us up.
"West Ham did, they made seven changes from the weekend, but I don't want to make excuses. I thought West Ham were the better team on the night and we were well beaten."