Just 12,793 spectators saw the Teessiders draw 1-1 with Huddersfield in the Sky Bet Championship on Tuesday evening, meaning more than 22,000 seats were unoccupied.
Mowbray told the Evening Gazette: "I think the people who are coming to the games at the moment are what I would call true Boro fans.
"They are going to be here through thick and thin and I can only thank them for their support.
"And I think the team, hopefully, showed that they are trying their best for them.
"We all want to win every game, of course. Hopefully that comes, this team clicks together and we win a lot of games."