Halliday was selected to start for Rangers at Hampden Park, but paid the price for his side’s poor start.
The central midfielder was taken off before half-time, with Rangers 2-0 down in the contest.
Halliday was clearly unhappy at the decision, and Murty has admitted that he can appreciate why the 26-year-old was annoyed.
“I wouldn’t have been happy. I completely understand his frustration but I was reacting to a situation in the game and I was looking at a different shape to the team” Murty said.
“Andy’s frustrated but I’ll see him in the week and have a chat and take things from there.
“It’s a frustration thing. If you deal with people in an emotional state, you get an emotional response.”
Things went from bad to worse for Rangers, after Halliday was taken off.
In the second-half of the contest they had Ross McCrorie sent off, as they fell to a 4-0 defeat against the Bhoys.
Whether Halliday will be kept in Rangers’ starting line-up for their next match remains to be seen.
Murty’s future is also unclear, with Rangers potentially looking to appoint a new boss at the end of the season.