"We had to battle hard because Arsenal are a great side," England defender Campbell told Sky Sports.
Tomas Rosicky and William Gallas squandered late chances for the Gunners - the first time Arsene Wenger's side have been goalless in a league game this season - while Benjani Mwaruwari might have snatched victory for Portsmouth when sent clear by Kanu only for Manuel Almunia to race off his line and force Benjani wide.
"They had a couple of chances at the end but it was a great shift by the lads," said Campbell.
"We wanted to get in their faces, put them under pressure and not let them settle on the ball. If you let them pass they will pass you to death.
"We had a couple of chances of our own but it was not to be. Benjani had a chance but their keeper came out quickly. It was a shame but that is the way it goes sometimes."
Wenger told Sky Sports: "They defended very well, they were organised not to concede.
"It was a very good defensive performance, their minds were completely on defending. We were not at our best today but gave absolutely everything.
"Credit to Portsmouth, they made it difficult for us. They played in one half of the pitch. I don't think offensively they had a special performance, they played with 10 players at the back and in the end they got the maximum they could from this kind of game."