Forest won 5-0 at the Stadium of Light to go eight points clear from the dropzone.
Pereira said afterwards: "Five goals, a clean sheet, I'm very happy the players, the supporters, the club and the staff. We deserve it because we played a fantastic first half. Congratulations to the people who do the set plays, they did a great job today. Recover, enjoy just a little bit and be ready for the next challenge.
"We decided to come here and press them because we are fighting for our life. When we are fighting we feel the need to do something, not to wait, we decided to press them and we did it very well and the fantastic goals from set plays.
"The second half was a bit different. Some injuries, some yellow cards, and with yellow cards you cannot be so aggressive on the ball. In the end one more goal, we did not concede, I am happy of course."
On Elliot Anderson's goal, Pereira continued: "He is part of our family. This is the moment to be with him, to support him, to help him everyday. He is a fantastic player with a strong, strong character. He is a fighter, a winner and he proved today again he deserves everything."
Pereira was also pleased for Chris Wood after he struck: "A fantastic striker. He knows everything about the game. How to hold the ball, how to assist, how to score, how to press, everything. He helped in the defensive set plays. He is a striker who can do everything.
"Morgan (Gibbs-White) also had a fantastic game, Igor (Jesus), Omari (Hutchinson), the defenders, the midfielders too. The speed that we showe, even from the bench, when we do the subs we kept the spirit."
Asked if they're now safe, the manager added: "It isn't enough. We need more points, we need to win more games and we need to keep our mentality."