The midfielder's new four-year contract with the club was met with skepticism from supporters, who have watched Pereira start just 11 games since making his debut five years ago.
However, Solskjaer says the 23-year-old "answered a couple of questions" against the Whites and believes he could kick on this season.
"We believe in the boy," Solskjaer said. "We gave him a new contract. He's answered a couple of questions today as well.
"He wants to learn, he listens, whatever you tell him he tries to put into his game. A couple of things today I saw were really encouraging.
"And you saw that today as well. If you give him game-time he will grow in confidence as well."