Penney, who took charge of the struggling Pirates eight days ago, watched as a defensive-minded Pools side frustrated his charges to keep them firmly rooted in the relegation zone.
Rovers enjoyed the better opportunities in a game where chances were few and far between. Striker Jo Kuffour saw two close-range efforts blocked before Hartlepool defender Peter Hartley was on hand to hack a James Tunnicliffe shot off the line in the opening period.
Hartlepool's best opportunity arrived at the feet of Antony Sweeney five minutes before the break, but the midfielder failed to connect with Andy Monkhouse's wicked ball across the face of goal when it looked easier to score.
Rovers striker Will Hoskins went close with a free-kick from the edge of the penalty area in the 75th minute as Mick Wadsworth's team seemed happy to settle for a point as the match crept to a conclusion.
Bristol Rovers 0-0 Hartlepool: Match Report - view commentary, squad, and statictics of the game as it happened.