The Newcastle loanee struck in the 54th minute of his first home start for Albion during Tuesday night’s 2-2 draw with Nottingham Forest.
Moore admitted it was a tough night for the winger, who struggled for the first 30 minutes before improving dramatically and impressing towards the end of the first half.
The 23-year-old then wheeled away in relief after side-footing home from eight yards out in the second half, and Moore is happy the deadline day signing is already up and running.
“I’m really pleased for him that he got the goal,” said Moore. “It was a tough night for him.
“He’s blessed with wonderful speed, and he’s got some tremendous quality, and that goal will hopefully do him the world of good.
“He’s got himself in there and dragged us back into the game.
“He kept going, it was really difficult, he didn’t have much room to manoeuvre, anything he did he had to fashion himself and create himself when we did get him on the ball.
“But he’s a player with tremendous pace and ability. He’s off and running for the club.
“Tuesday was a tough game but it was tough for all the squad members. He’s part of a team that has earned us a point.”
That strike was Murphy’s first goal of the season, but Jay Rodriguez slammed home his 16th of the campaign late on in controversial circumstances.
Albion were awarded a penalty when Dwight Gayle went over in the box despite no contact from anyone in red.
Rodriguez, however, stepped up to thump home his sixth successful penalty of the season and keep up his 100 per cent record from the spot.
“He practices them, that’s one thing he does do, he practices them a lot,” said Moore. “In that situation if you want someone to take a penalty it’s Jay Rodriguez, and he’s stuck it away for us.
“I’m pleased because we earned a point on a night where we were nowhere near our best.
“It’s a good sign to have. I’m delighted with the way they kept going.”
Ahmed Hegazi missed the game with a slight hamstring strain, but will be assessed before Saturday’s trip to local rivals Aston Villa.
“He had a little bit of a knock and I just couldn’t take the risk,” said Moore. “We left Gareth Barry out of the team, because of the volume of games.
“We’re playing every second or third day this month so you’ve got to manage the squad.
“We don’t get much to harbour on this one, we’ve got a local derby on Saturday, within the next 72 hours we go again.
“I’ll look at Ahmed in the next 48 hours and see if he’s ready to go.”