The Saints dropped into the bottom three, but could climb back out again with a win over West Bromwich on Monday.
If they claim all three points against the Baggies, that would leave Wednesday just one point above the relegation zone going into next Sunday's final games.
"The first thing I said to the players on Saturday was 'don't think we have done it, that's half the job'.' We are not taking our eye off the ball at any stage," said Laws, who has been in charge at Hillsbrough for a year-and-a-half after quitting Scunthorpe.
"We trained all week on how we were going to play and now we have to prepare them again for another massive game against Norwich.
"It was incredible. We had left ourselves in a position where we needed to win two games to get out of this and this is only half the job, but what a job we have done!"