The Welsh outfit earned a comfortable 3-0 triumph over the Canaries to move seven points clear of the relegation zone, but Monk has admitted that he was quick to tell his players that they still required more points to ensure safety.
The 35-year-old is quoted by Clubcall as saying: "We probably came in a bit too relaxed and I nipped that in the bud straightaway.
"We have to realise that we are still in a serious situation. We are not safe yet and we still need more points.
"Norwich was a big win for us. It was an important win and it has put us on a better points total. We can feel a bit more confident because we are edging closer to safety, but the key thing is that we are not there yet."
The win over the Canaries was Monk's second in 11 games in charge of the Swans.