With nine matches left to play, the Canaries are 14th in the Premier League table and have a gap of nine points between themselves and the drop zone.
However, despite having a safety margin of that size, Bunn has admitted that there is still work to be done before the players can rest easy.
"Here are games against teams around us, so our main aim is not to lose those games, try to take a point away from home and win our home games. If we do that then we will be all right," he is quoted as saying by the Eastern Daily Press.
"We don't see ourselves as safe. I think we need a couple more wins and then I think we will be okay. We have got some crucial games coming up."
Next up for Norwich is a trip to Sunderland on Saturday afternoon.