David Nugent, Joel Ward and Dave Kitson missed decent chances for Portsmouth, while Barry Robson and substitute Marvin Emnes went close for Boro at Fratton Park.
Mowbray said: "I'm disappointed with our ball retention, of course. The chances created were not what we would require.
"But sometimes football teams have to come and grind out results like that, particularly when we are at the bottom. The players will take a lot of confidence from the fact they could do that.
"I just felt the attitude of the team was right. We lost some early goals last week and the heads went down.
"This week we were always in the football match and (Marvin) Emnes could have won it late on when he went through one-on-one and the keeper made a decent save."
Source: PA
Source: PA