Martin Jol's side hit form during the second part of last year's campaign to record a ninth-place position and Schwarzer believes that the Cottagers should be aiming to repeat the achievement.
The 39-year-old told the club's official website: "To finish ninth - and we were very close to finishing seventh - when we started our first game in June was excellent. To have such a long season and still finish in the top half was a credit to everyone at the club.
"This season we want to again finish in the top half of the table and to continue to be an established Premier League team."
Fulham host Norwich City on the opening day of this season's Premier League.