Leadbitter had been linked with a move to the City Ground in the summer, with Boro believed to have turned down a number of bids from Forest, who also pursued the 27-year-old in the hours leading up to the transfer window closing earlier this month.
But the ex-Sunderland star remained at the Riverside and Mowbray believes all the transfer speculation is now water under the bridge and expects business as usual from Leadbitter.
"Grant is a very single-minded individual," explained Mowbray. "His whole life is about football, he wants everything done properly and he demands a lot out of the group.
"He is a very focussed guy and I had no fears once that window was shut that, as a Middlesbrough player, he would have any problems in applying his talent. It is a game he loves.
"He picked a great pass for (George) Friend's goal and he played very well last night."