The Welsh side will now hope to build on that as they host the Wigan side of their former manager Roberto Martinez on Saturday.
Vorm told Swans Player: "I think it was the busiest match I have ever played in.
"In the first 20-25 minutes we played very well, in the second half you hope you get some chances but they have such good quality players.
"If we had won or drawn it would have been a bonus, we don't need to win these kind of matches, Saturday is much more important.
"These are games we can win and if we play like we did in the first half, we can create chances.
"Wigan have quality, but not the kind of quality City have and it's important to play the same way Saturday and take the three points."