McDermott opted to play Varney in a central role alongside Ross McCormack and was rewarded with a two-goal salvo from the former Crewe, Charlton and Derby forward that secured a 2-1 win to lift Leeds six points clear of the relegation zone.
Leeds were 1-0 down at half-time but Varney's fifth and sixth goals of the season halted a run of four straight defeats.
"The gaffer gave a good speech at half time telling us to be positive and have no fear and that really showed," said Varney.
"It showed a lot about the bloke. He basically came in on Friday afternoon and stood in the dug-out. Most managers would have looked on and probably started (in the dug-out) on Tuesday.
"To see someone there telling us to 'pass, pass, pass' was a different outcome. It really worked for us and we are just delighted to get over the line.
"We felt we'd won the cup to be honest after a lot of disappointment and results. It was a real good feeling.
"For him to shove me up front shows he must have seen me before and know I can have a positive outcome up top.
"As a two (up front), I have not played there since I was with Nicky Maynard at Crewe. I enjoyed it."