The Toffees have finished in the top 10 six times in the last eight seasons but only once - in 2005 - did they make it into the top four.
Manager David Moyes has never had as much to spend on his squad as many of his top-flight rivals but Pienaar hopes that will be able to change in the future.
'I think the quality is here at the club,' said the 28-year-old.
'The only problem, like everyone seems to know, is the money issue - we need more players.
'Hopefully that will change in the next few years and the team can go on to challenge.'
As a result of recent struggles there has been speculation that David Moyes had taken the club as far as he could.