Tony Adams' side struggled to break down a resilient City defence and were made to pay for missing decent scoring chances – most notably Niko Kranjcar who headed wide when well placed just seven yards from goal.
Although City did not create too much going forward, Bradley Orr had an excellent second-half opportunity as his header was pushed over by David James.
And as a result, Pompey must now travel to Ashton Gate on Tuesday January 13 for the replay to battle for a place in the fourth round of the competition.
Although it wasn't a fluent performance from Pompey, they will perhaps feel they did enough to earn a victory on a difficult pitch.
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