Mowbray admitted: "We had a host of chances and missed them.
"We were through one-on-one two or three times and threatened the goal more than enough to have got something out of the game, but give Leeds credit.
"They worked hard and defended well without putting us under much pressure.
"They had a tough game against Chelsea on Wednesday and sent just about the same players out against us. They got a result so good luck to them."
Luciano Becchio turned the game on its head with two goals after Boro had taken the lead and even Mowbray was left purring at the Argentine's opening strike.
"Becchio's first goal was a great one. To turn and hit the ball as well as that showed great technique, but our own finishing needed to be more clinical," he added.