The Swans enjoyed long spells of possession in Sunday's historic derby against Cardiff, but they were unable to create many clear-cut chances as they slumped to a 1-0 defeat.
Michael Laudrup's side have scored more than one goal only once in their last eight matches, a 4-0 thrashing of Sunderland, and Vorm is aware of the urgent need for improvements up front.
The goalkeeper, who was sent off in the dying seconds at the Cardiff City Stadium, said: "It was a shame against Cardiff as I didn't have to make one save, but they scored from a set-piece.
"But we didn't create many opportunities. We are not creating much. You can miss chances in games, but we didn't create anything.
"We had shots on goal, but nothing serious. We have to work on that. We didn't scare them.
"We didn't create much against West Ham last week either, although that was a more difficult game.
"We know in the Premier League you don't get many chances anyway, but if we had played another day I don't think we would have scored (against Cardiff).
"This was like a typical 0-0 but you have to concentrate for 90 minutes and we did not."
Vorm also admitted he understood Mike Dean's decision to send him off for clipping Fraizer Campbell at Cardiff, although he claimed he touched the ball before making contact with the striker.
"I touched the ball first but the referee has a fraction of a second and my leg was high and I touched Campbell as well," said Vorm, who must serve a one-match ban when the Swans host Stoke on Sunday.
"It wasn't my intention to kick him, but once the referee has made that decision there's nothing I can do. He has to make those decisions so I can't complain.
"I was the last man because everyone was forward so I had come up to defend a big area. It was a shame, but it didn't make a difference in the end."
The defeat leaves Swansea only three points above the relegation zone, but captain Ashley Williams insists they will start climbing the Premier League table sooner rather than later.
"I'm concerned. I don't think we've hit the level where we were last season and it's something we've got to work towards," he said.
"I've been out for a few weeks and I've had the chance to see it from the outside and... I don't think we've really got to where we need to be.
"I remember a period last season - September or October maybe - where we weren't playing too well and then we turned it around with some big wins.
"We've been here before and we need to just work through it."