McDermott said: "Did we do enough to win? Probably not. Did we deserve to lose? Probably not.
"We got done at a set-play, which is disappointing to say the least and we didn't do enough with the ball. Without possession we were diligent and solid.
"I thought we should have had a penalty early in the second half, but their disallowed goal should have been given.
"These things happen. No-one could fault the players' effort. They kept going and showed real desire against a team that has cost a lot of money and the crowd didn't get on our backs."
Barton's disallowed goal came in the ninth minute, even though Leeds defenders Lee Peltier and Scott Wootton were playing him onside.
Leeds had a penalty claim rejected seven minutes after the break when Ross McCormack's driven cross struck defender Danny Simpson's arm just inside the box.
The only goal of the game arrived when Leeds made a hash of goalmouth attempts to clear Barton's free-kick and left-back Hill was first to react, lashing the ball into the net from a few yards out.
Unlucky Leeds captain Rudy Austin hit the crossbar deep into time added on.