Pompey controlled possession against a Gillingham side that were lacking ambition, but full of resilience.
But the hosts were ultimately unable to make the breakthrough on a grey and damp afternoon at Fratton Park.
They were the only side who really looked capable of securing all three points and looked particularly bright before the break
But Kenny Jackett felt that his troops needed to do more creatively to earn a third successive league victory.
The Blues boss said: “It was a frustrating afternoon after we played reasonably well in the first half and produced some good shots.
“Gareth Evans and Ben Close both tested the keeper, while we had plenty of corners and free-kicks in dangerous areas.
"We did fall away slightly and couldn’t create enough, despite being in control and looking solid at the back."
“The best of those led to Sean Raggett hitting the post and we felt we could really build on that at half-time, going on to win the game.
“But we didn’t do enough in the second period and an effort from Ellis Harrison and Lee Brown’s chance at the end were our best moments.
“Ryan Williams came on and added some energy, while Andy Cannon provided a different skill set, but ultimately it didn’t result in the storming performance we wanted.
“We did fall away slightly and couldn’t create enough, despite being in control and looking solid at the back.
“We’ve drawn 0-0 at home and want to be winning. To be the team we want to be, we have to use that defensive display as a base for more.”
Pompey were dealt a blow early in the second half when striker Brett Pitman had to limp from the pitch.
Jackett said: “He came off with a groin injury and we don’t yet know how long he’ll be out for. We’ll just have to see.”