Jack Harrison had Everton ahead on 33 minutes before Marshall Munetsi struck seven minutes later for the hosts.
A pleased Pereira said afterwards: "I’m very proud of my players, and we played a very consistent game against a difficult team.
“We tried everything to win the game and in the second half, we had a period with playing in the offensive midfield, creating situations and stopping the counter attacks, but for me, with this spirit I'm very confident (of staying up).”
The point has Wolves six points clear of the dropzone.
Pereira also said: “I like to see a team playing as a team, running together in the attack, running together when we must defend, and with personality and with confidence in themselves.
“Today, I saw everything, we showed everything and of course I'm not happy with the result, but in the end, it’s one point and one point can be important.”
Pereira was also happy with Munetsi scoring a first goal for Wolves since his January arrival.
He added, “He deserves it. He really deserves it. It was a pity that he felt something in first half and we cannot take risks with him. There was enough time and he asked the maybe it was better to stay out.
“But I think he deserves it because he's a player that has this speed that I like in a player. He gives everything to try to help the team, and in the end, he scored the goal and he will score more goals, for sure.”