McDermott lost his first game in charge of Leeds on Saturday at Birmingham - two straight wins were followed by a 1-0 defeat at St Andrew's - but results elsewhere ensured they cannot be relegated with two games left to play.
"We're definitely safe in this league now and I'm delighted with that," McDermott said after Saturday's loss. "The players have given us everything.
"That was job number one, two and three. I put myself on the line to come in at that stage of the season so that was the job.
"It was A, B and C - one, two and three and we've done that now and we're all delighted that we're now mathematically safe and can move forward."
McDermott, who steered Reading to automatic promotion last season, added: "That's a game we shouldn't have lost on Saturday, next season we won't lose games like that and we've probably lost games like that this season.
"There's no point talking about us playing ok and still lost the game, you don't win championships by just playing okay."