The Swans have lost three successive Premier League matches since reaching the 40-point survival mark by defeating Newcastle at home on March 2.
Some of the players have been accused of taking it easy since then, but Vorm insists they must keep pulling their weight in the final seven league matches.
"We have seven games to go and even though we have 40 points we have a lot to play for," the Holland international told the South Wales Evening Post.
"All the players have to look in the mirror and be honest with themselves, and ask have I really done everything I can to make this season end well?
"I look at myself and I can say I have done everything I can and if everybody does we can finish the season well."