The Tigers have been placed in mid-table for much of the season, and are potentially 90 minutes away from what would be the club's first FA Cup final, but are currently 13th in the Premier League on 33 points.
They face Stoke on Saturday at the end of a week where a win over West Brom was followed by a defeat to West Ham at Upton Park four days later.
"We are nearly there but no-one believes we are safe yet. Not at all," Bruce declared.
"We can't because football can be a really strange game. There are some big games coming up but if we play like we did at West Ham then I am sure we will be okay.
"We can take a lot of confidence out of the game. It was a really good performance and if we play like that for the rest of the season, we will win more than we lose."
Bruce's most recent outing lasted just 25 minutes, with the 29-year-old being substituted when Hull were forced into a reshuffle against West Ham.
Tigers goalkeeper Allan McGregor was sent off for the foul that led to the Hammers' first goal, a penalty by Mark Noble, with Bruce the outfield player to make way when replacement shot-stopper Steve Harper came on.
"It was so frustrating for me not to play. So, to get on and then have to come off after 25 minutes or whatever it was is disappointing," said Bruce, who was starting his first match for his club since 1 March.
"Obviously, as we went to play three at the back and with me a little bit in front, I had to give way. It is a squad game and you do your job. But it was frustrating."