Curtis Main's 81st minute header separated the teams and Mowbray said: "It's nice to get a win, it's been a while for us in the league and we need to keep the points ticking along.
"It's nearly 20 years since we won at home against Leeds. It's a good achievement for this team and we deserved to win.
"We competed against a team that you have to compete with and, on the balance of play, it was right we came out on top.
"Other games can be more of a football game but Leeds put you under pressure, don't allow you to keep the ball and it becomes more of a physical battle. But we came out on top of that."
Goalscorer Main was later sent-off for dissent after being adjudged to have handled to which Mowbray added: "Without being over critical of the official, he got it wrong.
"Curtis is a young boy who is starting his career. He came to us as a free transfer from Darlington and some of the things he can do are breathtaking at times."