Murphy lamented his team’s indiscipline in the first half, highlighting that as a contributory factor in leaving them with a mountain to climb.
“Our scrum held up reasonably well. Everyone knows when you come to South Africa your scrum is going to be under pressure so it’s an area we need to get better at.
“We had a way we wanted to play. We probably went away from that early on in the game but we got more towards what we were trying to do towards the back end of the half and in the second half.
“You have to stick in the fight here. Plenty of teams come here and kind of roll over.
“I don’t think we did that, which I’m really proud about, the way the lads stuck to the task.”
A Stuart McCloskey pass looked to have set James McKillop galloping clear on the wing to put Ulster in with a chance of what at one stage appeared a very unlikely victory but the Ireland centre was adjudged to have had part of his foot in touch.
“Stu’s foot was probably just in touch but if he gets that away earlier we’re going into the last two minutes with a lead. But that’s the breaks,” bemoaned the Ulster coach.
Murphy highlighted the breakdown as another area his side could improve on before next week’s meeting with the Stormers in Cape Town.
“We have to learn lessons but we will benefit from these tight battles come the end of the season,” he added.
The province’s Ireland internationals will return home to join up with Andy Farrell’s international squad, which assembles on Monday, while Murphy revealed that seven squad reinforcements would be arriving in Cape Town to bolster his side’s ranks ahead of the game with Stormers.