Pirates were unable to break down a disciplined low defensive block in a match where clear chances were rare and space was limited.
Durban City goalkeeper Fredrick Asare was kept busy to deny Mofokeng and Oswin Appollis, with the visitors remaining resilient throughout especially in key second-half moments from close range.
Mofokeng also suggested the approach resembled "bus parking" and described Durban City as highly physical, aiming to disrupt Pirates' rhythm and break up attacking flow.
"It was very difficult from the very beginning to the end, they came to defend and they did it very well, I think they were doing it the whole week," Mofokeng told SuperSport TV.
"We also tried to create chances, we didn't convert them. We could have just converted our chances, so ja we could be having a different conversation here.
"But it's what we have to expect in every game because we're doing good, obviously people will come and want to take us out of the game. We must just be focused and keep on going and don't change how we play."
The result leaves Pirates two points behind Mamelodi Sundowns heading into the final matchday.
They must beat Orbit College in Mbombela next Saturday and hope Sundowns slip to have chance of title.