Boro quickly clawed back an early Norwich opener from Grant Holt as Julio Arca's shot took a wicked deflection off Russell Martin, then had a second half strike by David Wheater ruled out for shirt-pulling, while Justin Hoyte hit the post late on.
It came hot on the heels of a 1-1 draw at in-form promotion-chasers Leeds in a New Year's Day game that Boro also bossed only to be pegged back in stoppage time.
"We are disappointed," said Mowbray. "Some people are saying that is two good points against top of the table sides but we feel it could and should have been six points from those two games.
"The way we have played and the fact that we have come away from those games believing we should have won both shows we are more than capable of competing with the top teams in this league.
"It is indicative of where we are as a team right now. I hope people can see the steady improvement in performances since I came here. The development in the last six weeks has been encouraging."