The Edinburgh lock returns to the Scotland starting 15 against Ireland in the Six Nations on Saturday after being banned for the famous Murrayfield victory a fortnight ago.
Murray was unable to have his sending-off against Wales overturned and, despite receiving letters of support, was miserable watching his team-mates triumph play without him.
But on his return to the dressing room, he was chuffed to hear the level-headed Scots criticising themselves, which shows just how far they have come under Frank Hadden.
Murray said: "It was a tough game to watch and I had to try and distance myself from that.
"I tried to enjoy it as a spectator but it was very difficult to watch.
"It's massively hard because there's nothing you can do to affect the outcome of the game.
"It was a tough 80 minutes but in the end it was really good that the boys won the game.
"It was actually harder after the game because everyone was celebrating. You want to be happy but you are just gutted that you're not involved.
"But it was quite nice to hear when I came into the dressing room after the game that the guys were saying we should get on the ball more and use it better."
Murray believes it is that collective willingness to improve which could drive them on to victory at Lansdowne Road and then possible championship glory.
Scotland have not beaten their Irish counterparts on their own patch since February 1998, while their last away win in the Six Nations was in Italy back in 2002.
But Murray said: "It's been a massive turnaround and it's all to do with confidence.
"We have a lot of grounded people in our squad so we won't lose our way and start thinking we're better than we are.
"This is going to be a tough weekend but the players are striving to improve all the time and a win is possible.
"It just shows that the players want to keep on growing and getting better, which can only be good for Saturday."