Wales remain without a win after a 14th successive Six Nations defeat, having led Scotland until the 75th minute before slipping to another narrow loss.
But for Murray, who featured as a replacement, there was a clear shift in intent and attitude compared to earlier rounds of the tournament.
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“It’s frustrating seeing the boys go out and put on a good effort, and not come away with the result,” he said as the Wales squad use their break weekend to prepare for next week’s trip to Dublin.
“We didn’t play the way we wanted against England and France, but Scotland was a really good shift for us.
“We wanted to take the game to them more rather than wait for opportunities, and I thought we did a really good job of that.”
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The Scarlets back believes that proactive mindset — taking the initiative rather than reacting — is something Wales must carry into Dublin next Friday.
While encouraged by the team’s direction, Murray is also battling to regain a starting role.
The 24-year-old began Steve Tandy’s tenure as first-choice full-back but has been left out of the XV during the Six Nations, with Louis Rees-Zammit preferred at 15.
At 5ft 7ins, Murray has inevitably faced scrutiny in a tournament where aerial contests have been decisive.
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Yet he is adamant size and stature alone should not define selection for Wales head coach Steve Tandy.
"I'd like to think I am in the squad for a reason," said Murray.
"I bring something that other players don't, so I just hope I get that opportunity.
"Steve has been transparent and kept it clear in terms of selection, so I just have to train my way back in."
He added: "I play differently to somebody who is 6ft 5ins but I don't think someone my height can't play.
"When I have played I've done pretty well and made a case for being able to play as a short player.
"I still think any shape or size can play ruby, things change tactically but I still think that saying goes strong."
Murray points to examples across the international game to reinforce his belief that size is not everything.
“When I have played I’ve done pretty well and made a case for being able to play as a short player.
“There’s other players like me, such as (Scotland winger) Darcy Graham, who is a class player and was in the Lions last year.”
The modern full-back role, however, brings unique challenges, particularly under the high ball where players are often isolated.
“It’s a tough job. Without people being able to escort or block it does become just a straight one-on-one in the air.
“We’ve done a lot of work here about how many balls actually get caught cleanly and it’s quite a low percentage.
“So it’s more just about we’re focusing on trying to make a collision. Don’t shy away from the contact in the air, and just try and win the space early.
“You’ve got to try and have the mindset of winning the collision.”
