Matt Connolly's 19th-minute header was the match winner as Malky Mackay's side moved above the Boro into second spot in the table.
Mowbray also refused to attribute any fault in his decision to pick Lukas Jutkiewicz ahead of Marvin Emnes.
He said: "Marvin is a good player but so is Lukas. Managers live and die by their selections. I don't regret picking him.
"I thought we played pretty well. There is a long way to go in the rest of the season and if we perform like we did here for long spells then we will be okay.
"The longer the game went on, the chances came and went for us and, ultimately, we didn't manage to stick one in the back of the net."
Middlesbrough last week