The former Burnley and Everton manager has instilled some steel into Forest, and that was evident at the City Ground as they responded strongly to falling behind inside 15 minutes.
"It's a sign of the mentality changing. We were on a run of one loss in five now," Dyche said after Forest snapped a nine-game winless run in the league stretching back to August.
"It's good to get that winning feeling back. Awkward game for many reasons. We had to use the squad. We have to work with the players and continue the growth."
Lukas Nmecha gave Leeds the lead in the 13th minute, but Ibrahim Sangare levelled minutes later.
Captain Morgan Gibbs-White headed Forest into the lead from substitute Omari Hutchinson's cross, and Elliot Anderson wrapped up the points with a late penalty.
Forest remain second-from-bottom but are now only one point behind 17th-placed Burnley and three behind 14th-placed Newcastle United.
They have lost just once in five games since Dyche arrived, having lost seven of their previous nine in all competitions, but he said the key now was raising the standards further.
"Now we're hungry for more. Don't just accept that like: 'Oh well, that's all right'," he said.
"It's not all right. All right gets you nothing if you want to achieve things, all right is going to get you nothing. So we push for more than all right."
For promoted Leeds, a fourth defeat in five league games left them hovering just above the drop zone, and manager Daniel Farke said the small margin for error in the top flight was something his players had to learn.
"Football games on this level are decided with small details. We have to make sure we are more switched on," Farke said. "I did expect a tricky period. We have conceded too many goals in the last two away games."