A 70th-minute goal from David Nugent gave City their fourth league win in a row and sent Middlesbrough to a third consecutive defeat.
Foxes goalkeeper Kasper Schmeichel added to Boro's misery by saving a penalty from Marvin Emnes in stoppage time.
Mowbray, who revealed that because of the weather it had taken them two hours to travel two miles from their hotel to the ground, said: "We are very disappointed as I think we did enough not to lose the game.
"We created enough chances to get something out of the game. We played against a good side who have been free scoring all season going forward.
"They hit the woodwork three times, but we had some really clear-cut chances as well.
"We didn't stick them in the back of the net and goals change games. We have to be more clinical and it is a very frustrated dressing room.
"To have a penalty going into injury time and not score is very frustrating. But there a lot of positives, enough to know we can go on our travels and win.
"We have got nothing to fear and we go into all games knowing that we can win them. But we need to be more clinical."
- Sports & Recreation