The Teessiders find themselves seven points shy of the play-offs after a disastrous run of 12 defeats in 16 Championship games, during which time they have accumulated just eight points.
However, Steele insists neither Mowbray nor his players have given up hope of a fightback into contention.
He told the Northern Echo: "You can tell every time you speak to him that he is hurting.
"Everybody is hurting because we all wanted this to happen. We all wanted promotion. He is trying his hardest to turn things around.
"There is still a glimmer of hope there and we are more than capable of winning the next five games, even though we have not shown that in recent months."