The former Sunderland man scored the spot-kick eight minutes from time to give his side the win, and he talked up the importance of the victory after the game.
"It's a massive three points for us," Leadbitter told Sky Sports News.
"Our performances have been good but results have been quite poor really and it shouldn't be for a massive club like this, so it was a big win and we go to Derby County on Tuesday night now and try and win there.
"[Aitor Karanka] has come in and he wants high standards every day from us, which is good, so we'll come in tomorrow and get ready for Derby."
New boss Karanka was taking charge of his first home game at the Riverside.