The promoted Hammers currently sit eighth on the table after 15 matches and Jaaskelainen believes they can keep chipping away and push for a Europa League position just like Bolton did when the Finnish gloveman in two back in the 2005/06 and 2007/08 seasons.
"At Bolton I remember we began the season on fire, but then couldn't win for seven games, but still finished in the top six," he told reporters.
And Jaaskelainen feels that consistency is the key for West Ham to achieve success this term.
"It's all about consistency. Everyone makes mistakes, but as long as you're consistent, you will do well," he added.