The Cottagers finished ninth in the league last term after kicking off their campaign in June with Europa League duties.
After such a hectic schedule, it was a good effort by the Southwest Londoners to produce a top-half finish and Australian international Schwarzer is expecting more of the same as the new season approaches.
"It's been going well," he told the club's official website regarding pre-season. "We've had two pre-season camps - one in Germany and one in Switzerland - and they've been good.
"Overall we were all very satisfied with the way the season ended up.
"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.
"It's going to be tough and every season it gets tougher. Teams are investing in new players and the quality of the league is always getting better but we need to make sure we continue doing what we've been doing the last couple of seasons."