The Black Cats stunned the Blues 2-1 in London on Saturday.
Afterwards, Cucurella told the club's website: "It’s a really tough one to take. We are all very disappointed, of course.
"We need to improve with these matches. I think we need to learn to manage the game better. We scored early, dominated at that stage but then we let the opponents back into it and I think we need to learn to kill games off when we are on top.
"We scored the first goal, and I think we should have scored a second one when we had the chance. We need to learn to be better against teams that come with a gameplan such as Sunderland, where they stay very narrow and compact.
"The good thing is that it is still early into the season. We have many games where we can improve and we have plenty of time to do this, and secure more points."
Cucurella also conceded: "The goals we conceded, we know we can manage these situations better. We know that a lot of teams are trying to use long throws more and we need to manage them better.
"We worked on them yesterday because we knew Sunderland will look to use long throws and be direct from set-pieces. I think maybe we relaxed a little bit, and they punished us. It’s no excuse, we need to learn from this and make sure this situation doesn’t happen again.
"Then with the second goal, again, I think we need to manage things better. It’s true that we always look to win, especially at home, but we’ve been caught out on the counter-attack and been punished. It’s small mistakes but ones we need to learn from.
"The good thing with football is that you can always put things right quickly. We have another game on Wednesday and it’s an opportunity for us to get back with a win."