The 29 year-old concedes that Saturday's 1-0 loss against Norwich was hard to take because of how late the winning goal came.
But Bruce insists that the spirit in the squad remains upbeat despite the setback, which was their third Premier League defeat in a row.
The Tigers currently sit in 11th position, just four points clear of the relegation zone, and will looking towards the upcoming fixture against Crystal Palace in order to pick up points to ease away from the relegation zone.
"We're not safe. I don't think any team from 10th to the bottom can say they are safe," Bruce said in The Sun.
"There are only five points in it and we know it's not going to be easy.
"Losing at Norwich is disappointing and to concede so late in the game was just a sucker punch.
Talking about the upcoming game against Crystal Palace, Bruce added: "We just need to make sure we don't get too downhearted and take the positives from the game into our next league game against Crystal Palace."