The Toffees endured a tough February and sit in sixth place, but their South African midfield schemer is confident they could still earn a place in continental competition.
Goals from Marouane Fellaini, Kevin Mirallas and a wonderful strike from Pienaar ensured the home side claimed a valuable victory against a relegation-threatened opponent and maintained its faint hopes of claiming a Champions League qualification spot.
Despite collecting just one point in the Premier League during February, Pienaar is hopeful that Everton can rekindle its form and win a place in Europe for the first time since the 2009-10 season.
"We haven’t given up on Europe," the South Africa midfielder told Everton's official website. "Hopefully we can sneak in by the back door. There is a bit less pressure on us to push. We will see how the other teams do but hopefully we can get there.
"Europe is important for the supporters. I think they enjoy going away! For me, it's really good to play in European competition. After the Premier League there are only two bigger cups – the Europa League and the Champions League. All the players want to play in them, so it's important for the club that we get European football."
Pienaar notched his sixth goal of the campaign in the defeat of the Royals with a sweetly struck left-footed effort from the edge of the penalty area which the 30-year-old was delighted with.
"It was one to remember, especially with the left foot," he said. "I didn’t really decide that that was what I would do. When I got close to the 18-yard box, things started to open up and it bounced quite well to hit it so I took the chance and it went in.
"But most important was the win. We hadn't won in the league for a while so it felt good to get all three points again."