One of United's biggest problems this season has been their lack of goals, scoring just seven times in eight league games as they search for an adequate replacement for Luciano Becchio, who went to Norwich in January.
Matt Smith at least added some punch when he got off the bench to nod in an 80th-minute consolation against the Clarets, but around that Rodolph Austin, Ross McCormack, Dominic Poleon and Luke Varney all floundered in the box.
"We need someone to grasp the nettle and take up the responsibility of scoring," McDermott said.
"We haven't scored enough goals, especially at Elland Road. It's a worry because someone has to try and take that responsibility. I said to the players, the worst thing that can happen has happened. They lost. That's it. I give them the license to make things happen."
McDermott has had to face few on-field challenges since taking the Leeds job in April, but three defeats out of four could be viewed as one.
He conceded Burnley had presented him with problems he had not faced to date, and wants his players to start showing more creativity in a bid to prevent it happening again.
"We were 2-0 down and we can't play like that. Burnley were good, credit to them, but they were soft goals for us and good ones for them. We got beat up by their strikers and that's the first time it's happened since I've been here," he said.
"The midfielders need to get on the ball more. I give them the license. We need to keep working them and drilling them."