The Swans players have been right up for the likes of Manchester United, Liverpool and Arsenal but Vorm feels they have taken clubs such as Blackburn Rovers (4-2 loss on the weekend) a bit easier and he wants that stamped out.
"We started with a good mentality, but in matches against Blackburn, Norwich and Wolves we have to bring more," he told the South Wales Evening Post ahead of the visit from Fulham on Saturday.
"As a team we have to do more. We have to give more in these matches.
"Any player can give more against Liverpool. It's easy to do that.
"We have to learn really quickly because the competition is going so fast and Blackburn are coming up fast now.
"If you want to win matches like Blackburn you have to have a better mentality.
"We must learn from it and make sure we win our games at home. The pressure is on us. Saturday against Fulham is very important."