Murphy said it was “hard to sum up” his emotions after the incident-packed draw with Stormers at Affidea Stadium.
Eleven tries were scored in an end-to-end encounter, with the award of a late penalty try to the away side causing controversy.
Nathan Doak thought he had won the game for Ulster by holding up Stormers winger Leolin Zas as he looked to score, but, upon further review, Doak was penalised for shoulder-to-head contact, received a yellow card, and a penalty try was awarded, decisions which Murphy was frustrated with.
“You look at the collision or the lack of collision and you go, ‘well, we can find at least another five occasions that that isn’t looked at during the game’, so that’s quite difficult to take,” he said.
“Is there head contact? Is it direct? The referee has to make the decision in regards to that, but a very disappointing way to take a victory away.
“We look at that last sort of two minutes or so from a defensive point of view and we didn’t defend well enough, that is for sure, but we’ve got one really big, strong, physical and attacking team coming at us as well.
“Over the 80 minutes, I thought the way we adapted to the sort of things that went against us was really good. I thought we scored some brilliant tries as well.
“I thought the character that was shown within the team over the last couple of weeks has been really good. So, we need to take it on the chin and just get moving forward into the next one.”