The Toffees currently sit third in the English top flight following four wins, one draw and just one defeat in their opening six fixtures.
But the South African believes that the Merseyside outfit have achieved nothing yet and must continue working to stay ahead of their rivals.
"We are not there yet. After 10 games we can say how well we have done," he told the Liverpool Daily Post.
|16/1||Everton are 16/1 with PaddyPower to beat Wigan 3-0
"We have been working really hard and it's important to get the points to make sure we break away from the other teams below us. But there's still a long way to go."
The 30-year-old also hailed the quality amongst the Blues squad and claimed that the club can go on to qualify for Europe this year.
"[The start] hasn't exceeded my expectations," he observed. "The manager asked for us to start the season well and, to be honest, the way we ended last season, it's no wonder we've carried that form on.
"I said when I rejoined Everton that, with the quality we have and because the team has been together for a few years, I think it is time for us to achieve something.
"Finishing in the top five or top six is something we have to push ourselves to deliver. We have to push the bar that bit higher."
Pienaar was particularly effusive in his praise of team-mate Marouane Fellaini, who has enjoyed a blistering start to the season, including scoring the winning goal in a 1-0 win over Manchester United.
"He’s a big guy but technically he is great with the ball so he brings something different," the midfielder enthused. "When we played Man United we knew it was going to be a hard game if we wanted to match them possession-wise but he was central to us doing that.
"He comes out of the tunnel in front of me every game so I don't see much when we walk out! But when I see him I feel confident.
"He brings that presence with him out on to the pitch and that lifts the players around him."
|"When I see him I feel confident. He brings that presence with him out onto the pitch and that lifts the players around him"
- Steven Pienaar on Marouane Fellaini
The Johannesburg-born midfielder, who announced his retirement from international duty on Tuesday, noted that the camaraderie in the Everton camp has borne out their good form.
"The team spirit is very healthy," he continued. "We all want to work for each other and we sense that maybe this season something special will come.
"We need to keep on going and not get carried away. There is always a good vibe in the dressing room, there are no egos. I think that is important.
"If there are egos there are going to be problems. Here there is one boss and it works."