Murphy, a £1million buy from Crewe last summer, has struggled to live up to his price tag this season but he was outstanding as Leeds, whose players have now received the deferred final slice of their March wages, ended a run of five defeats.
McDermott, whose position has come under pressure, expressed hope after the 2-0 victory at Elland Road that Leeds would now see the best of the 24-year-old midfielder.
"Luke's two finishes were excellent and he could have scored before our first goal. You need the right mentality to play at this ground," McDermott said.
"Luke scored a lot of goals for Crewe. He was there from about 12 years of age, playing with the same players while coming through the ranks. Then he came to a massive club like Leeds and it can take time for players to adapt."
McDermott is confident Leeds will not have to worry about relegation now, and he was delighted to see the dawning of a new era at Elland Road under the guidance of Italian Cellino, after a long period of uncertainly over the club's ownership.
"The win was a great relief. It was a big result for us," McDermott said. "We are on 50 points and that should be enough, but you can't think like that. I can only think about our next match at Barnsley.
"Thank God we have got Massimo Cellino in charge because I didn't know where this club was going. The fans gave him a really good reception and I am delighted for him. We've all got paid and this club feels like a different, more secure place now."
Blackpool, with just two wins from their last 26 games, are two points and two places above the relegation zone.
Assistant Blackpool manager Malky Thomson said: "We are disappointed that we came away with no points at all, but the level of endeavour from the boys was great.
"We still have a lot of self-belief and we have to carry that on against Burnley. Our player-manager Barry Ferguson is totally self-motivated. Barry has the bottle to go out and play when the pressure is on. He will have no sad faces around the place and he was massive for us today.
"Unfortunately, Luke Murphy is not bad either, is he!
"Leeds managed to take their chances and we didn't. That was probably the only difference. I can guarantee the players at Blackpool are utterly professional in their outlook. We haven't set ourselves a points target. We are fully focused on getting the right result from our next game against Burnley."
Murphy showed finishing of the highest calibre, switching the ball on to his left foot to slot the ball in from the corner of the six-yard box in the 21st minute for the first and cleverly dinking the ball over goalkeeper Matt Gilks with 17 minutes left.
Leeds goalkeeper Jack Butland denied Blackpool a consolation goal by stretching to tip Gary MacKenzie's header over the bar with five minutes left.