The Sons continued their remarkable run of form under their new manager with a 3-1 win over Hamilton on Saturday as they made the most of defeats to relegation rivals Cowden-beath and Airdrie United.
Murray said: "It's pleasing that we now sit eighth and it's just reward for the effort the players are putting in.
"Getting off the bottom is a psychological boost for everyone. We have a foothold now, but we won't get carried away.
"I said when I came in I wanted our ground to be a place where other teams won't want to come.
"We need to make it very difficult for others to come and win the points and in that respect it's another box ticked.
"It wasn't a pretty game on Saturday, but we are showing grit and determination and the players must take a lot of credit for turning things round.
"We did though score some good goals. Chris Turner's finish for the opener was top drawer and Mark Gilhaney's pass into the net for the second was also quality.
"It's Livingston we play next and they have some good footballers in their team allowing them to adapt to different formations.
"We are now able to compete on our own terms and it's another game we are all looking forward to."
Meanwhile, Sons striker Pat Walker is set to join Div Two drop-zone battlers Albion Rovers after he had his contract at the Bet Butler Stadium terminated and defender Ross Forsyth has agreed a move to Stirling Albion after finding himself out of favour.