The Toffees' hopes of claiming a place in the Champions League took a knock in February but they still have an outside chance of reaching fourth spot in the Barclays Premier League.
Even if they do not make it into the elite competition, they should be strong contenders to bring continental football back to Goodison Park via the Europa League, through league position or the FA Cup.
Everton, sixth, boosted their league prospects with a 3-1 win over struggling Reading and are now looking forward to a cup quarter-final against Wigan next weekend.
Pienaar, who scored a stunning second goal as the Royals were overcome at Goodison, said: "Sometimes you have to go through the back door, so there is a little less pressure on us now.
"We will see how the other teams do and hopefully we can sneak in.
"I think it is fairly good to play in European competitions. After the Premier League there are only two bigger cups - the Europa League and the Champions League.
"All the players want to play in it and it is important for the club to get European football.
"We will just see. The cup is the shortest route to European football. Next week we are also at Goodison so hopefully this can be the place that gives us the passport to European football."