Papiss Cisse struck the opener for Newcastle in the 31st minute and Yoan Gouffran fired the decisive second for Alan Pardew's side in the 67th minute to set up a fourth-round clash with Manchester City at St James's Park.
But McDermott was left to reflect on what might have been after insisting his side should have had a penalty at 1-0 following a coming together between Newcastle defender Fabricio Coloccini and big Leeds striker Matt Smith.
The tie proved more tricky for Newcastle than the scoreline suggests with Leeds almost shocking their hosts early on when Ross McCormack saw a fifth-minute chip come back off the crossbar with goalkeeper Tim Krul beaten.
McDermott said: "To not get the penalty was galling, but that's how it is sometimes. But we were right in the game, we felt, all the way until the second goal, and the second goal kills you.
"But they have got a good side here and they have got a good manager, and they played some good stuff. But so did we."