Mustapha Carayol scored the only goal at the Riverside Stadium, earning Mowbray's side three points, but the Boro boss is not convinced his side can overturn a six-point gap.
"I thought we worked extremely hard and if anything we could have scored more late on when they were really over-gambling to score," he said.
"In the world of football if you get beat, you must be rubbish but if you win, you're okay.
"But our performances as a team have not been as bad as the run we've been on.
"Ultimately we'll finish where we probably deserve to and hopefully that's in the top 10 and pushing on to get some confidence out of the last few games.
"It's worth mentioning the supporters who've stuck with the team over the poor run we've been on. Hopefully they enjoyed tonight."