Murphy had been waiting patiently for an opportunity on his return to the Stadium of Light and it arrived in the closing stages when Tyias Browning’s errant pass left Forest in possession.
Barrie McKay fed him in the area and the Irishman skipped past Browning before drilling a clinical low finish into the corner.
Murphy’s goals helped Newcastle win promotion from the Championship last season, and while he might turn 35 in March, he remains as effective as ever.
Warburton said: “Daryl offers you a physical threat, but he’s also a very good technical player. He did a very good job for the team, and we would have wanted that chance to fall to him.
“It was a very good win for us. There’s no doubt that both teams were on the back of a bad result, and I thought both teams played with a bit of fear.
“We thought Sunderland would come out hard and fast, and they did, but we dealt with that. We had to defend our goal with a passion, and then we were gradually able to play a bit more ourselves.
“We had to work very hard, and credit to the lads for doing that. We defended our goal with a real desire and sometimes you have to do the ugly side of the game well before you can play.
“This league is relentless, but the progress within the squad is clear to see. We’re improving, and we will continue to get better.”
Sunderland’s defeat leaves them just a point above the relegation zone, and means they have still not claimed a home win in the whole of 2017.
Nevertheless, Simon Grayson felt there were signs of improvement from Saturday’s home defeat to Sheffield United and remains optimistic his side will return to winning ways sooner rather than later.
Grayson said: “It’s probably the most frustrating result we’ve had because we didn’t deserve to lose that game, without a shadow of a doubt. I thought the players responded from Saturday and showed a lot of bravery with and without the ball, which we asked them to do.
“They responded in a confident manner from the weekend’s result, and it’s a big kick in the teeth when you lose a game like that because we didn’t deserve that. It happened though.
“We didn’t get the breaks when we wanted them, with things falling in the 18-yard box, and the one mistake we made over the whole of the course of the night, we got punished for it.
“When you’re losing games, that can happen, and unfortunately it’s happened tonight. But there were a lot of positive signs from the team and I was really pleased with how they responded from Saturday.”