Having guided Hull to promotion from the Championship in his first season at the helm, Bruce kept them up last term and enjoyed a run to the FA Cup final.
However, with six games remaining Hull are just two points above the relegation zone, with Saturday's 2-0 loss at Southampton their sixth match without a win.
It has left Bruce in no doubt that his side are in a fight for their top-flight lives.
"We have had a wonderful three years," he said in quotes reported by the Hull Daily Mail.
"But I always had something in my water thinking this would be the most difficult challenge.
"All of a sudden, there was an expectation. And we haven't been able to live up to that. But I still hope we have enough to keep us out of trouble.
"The supporters realise we are in a bit of a scrap. We are Hull City and have only been in this top league for four years.
"No-one was naive enough to think it was going to be easy. From what I grasp of the city, the fans have been right behind me.
"Of course, when results go against you, there are going to be a few people who are shouting for the manager. But our fans came down here in droves and everyone is up for the challenge. And I am sure we can do it."
Hull are not in action again until the trip to Bruce's former club Crystal Palace on April 25, by which time they could have dropped into the bottom three.
