Leeds had failed to muster a single chance on goal when Bournemouth were harshly reduced to 10 men in the 31st minute.
Goalkeeper Ryan Allsop was adjudged to have brought down Leeds striker Noel Hunt in the penalty area and was shown a straight red card by referee David Coote.
But Bournemouth's replacement keeper Darryl Flahavan saved McCormack's subsequent penalty and misfiring Leeds went on to make hard work of their first win in five matches.
"It reminds me of a game when I was permanent manager at Reading when I first got the job," McDermott said. "We played Barnsley and won 1-0 and I thought then that the only thing that mattered was to win.
"As caretaker we hadn't won for five, we drew two and lost three and we were struggling at the bottom of the table, but we beat Barnsley and went on to win eight on the trot.
"I'd take that again! But we deserved to win. That's never an easy game, they've got nothing to lose, down to 10 men.
"We showed great guts, we were nervous towards the end when they got back to 1-1 - but we didn't go under and created a lot of chances.
"I definitely think we deserved to win. The only thing that mattered in this game was the result. Nothing else."
Allsop's controversial dismissal proved to be the game's turning point, but McDermott insisted referee Coote made the correct decision.
"I've seen it back and it was a penalty," McDermott said. "He (Hunt) was going to score. It was a definite penalty.
"I went through the mill because it was important to get that result.
"We've got it and we'll be better for that on Saturday (against Derby)."