The Cottagers have twice finished in the Premier League top 10 over the past three seasons and also made it to the Europa League final in 2010.
Schwarzer has proven a key figure during Fulham's recent success and has urged his team-mates to continue where they left off next season.
"We've just got to keep backing up what we've been doing over the last few years," he told the club's official website. "The last three seasons have been - for Fulham Football Club and a lot of us personally - fantastic.
"It's possibly been the best three years in a lot of our careers. We need to continue that run.
"We believe that we belong in the top half of the Premier League and we like to think that we can mix it in Europe every couple of seasons.
"The expectation levels are always higher. When I first came here, the club had just avoided relegation with 15 minutes to spare so anything above that was a bonus.
"To then finish seventh, then have such a great run in Europe and finish eighth last year means the expectations are there.
"We, as players, acknowledge that and we know that we need to live up to them.
"So far it's been a great challenge. If you look at the history of the club and how much has been accomplished, particularly in the last three years - it's been outstanding."
Schwarzer has been with the west London club for three seasons now and was keen to praise Fulham chairman Mohamed Al Fayed for helping the club to their current position.
"The chairman's been 100 percent supportive and the club wouldn't exist in the position it is now without the support of the chairman," he added.
"He's always been there and he's always been rock-solid for the club. He's always looked to progress.
"In the years that I've been here, I've seen a lot of progression."
Meanwhile, Fulham have confirmed that its development squad will compete in the Premier Reserve League South next season.
Billy McKinlay's team will face the likes of Manchester United, Chelsea and Arsenal over the course of the 2011/12 season, with home matches taking place at the club's Motspur Park training base.