The Swans have slipped to defeats against West Brom, Arsenal and Tottenham, and while they look safe in ninth place in the overall standings with 40 points, Vorm wants to return to winning ways.
Norwich have the best record of any Barclays Premier League team against Swansea since the two sides were promoted, having won all three of their fixtures.
"It's a very important game because we have lost three in a row," Vorm told the South Wales Evening Post. "We had the same problem around the same stage last season when we got to 39 points (and lost four successive games).
"We have to make sure we have a good week's training and there is no option, we cannot lose. That has to be the mentality against Norwich.
"We have shown that mentality all season to beat almost everybody and now we have to look in that mirror, be honest and do everything to win a game."
Vorm, however, is at a loss to understand why they find Norwich so hard to beat.
"It is hard to say why they have done so well against us because they are not a top, top team, but they work hard all the time and we have to start by matching that," he said.
"We have lost quite easily twice to them, so we know it will be a very tough game.
"We all know what we have to do to beat them - we need to start off well, we have to be 100 per cent focused on scoring the first goal and we have to try to make sure we don't concede."