Swans lost 1-0 at Emirates stadium on Saturday.
Vorm said: "You come inside the Emirates and think 'OK, 60,000 people and the atmosphere will be great.' But they play with no confidence and with the new players it is hard for them to fill in the places.
"I think Mikel Arteta did well but although they have the quality they do not have the confidence.
"Manchester City have the confidence - and the money. They have a group of 22 or 23 players who are all world class.
"For Arsenal it is hard and they feel a lot of pressure, including from the crowd. It is not easy to play here but it was a good lesson for us to play and there are 34 matches to go and we must score!"