Scott Hogan and Ian Henderson scored the goals that saw the League Two club spring an upset at Spotland as Rochdale reached the fourth round for the first time in 11 years.
The 2-0 defeat extended Leeds' winless run to five matches in all competitions and McDermott called for investment in the Championship team after what he stated was a low point in his career.
"I would probably say that is my worst moment in football," he told BBC Radio Leeds.
"This will be a driver for me in the coming weeks. We need to invest in this team, it needs help. We seem to have run out of steam.
"We have to do it for those who travelled today and (we are) desperately, desperately sorry we put on a performance like today. Rochdale played well and it is their day."
While McDermott had no complaints about the result, Rochdale counterpart Keith Hill also felt his players deserved their moment in the spotlight.
"It's a tremendous win. We had a gameplan and the players executed it superbly," he said.
"The players trusted me and each other. No-one can argue we didn't deserve that win."
