Mark Gilhaney, Alan Lithgow and Bryan Prunty all found the target for the Sons but it wasn't enough to prevent them slipping to defeat against the Lions.
Murray's side remain eighth in the Irn-Bru First Division standings and the Bet Butler Stadium boss said: "We are disappointed with the result because we have lost at home but in terms of their effort and the quality of the performance, I thought we were excellent again.
"In the first half in particular I thought we controlled the game and to be 1-0 down at half-time was ridiculous really.
"You have to give credit to Livingston because they have come away from home and scored four goals and they got the three points so we have to move on to next week.
"We came in at half-time disappointed but we regrouped and started really well in the second half.
"We recovered well and got ourselves back into the game with a terrific goal from Gilhaney and then they scored a soft goal from our point of view and then what was a wonder goal to be honest.
"We said at half-time about the importance of staying in the match as long as we could but our two late goals came to nothing.
"Overall, in the last six weeks we are delighted."