But Pompey boss Steve Cotterill felt he should have left Ashton Gate with all three points.
Cotterill said: "Bristol City were the better side in the first half, but we did much better in the second and had some great chances to win the game.
"Considering Bristol won away at Leicester in midweek it doesn't look a bad point for us, but I'm disappointed we didn't get all three.
"They deserve credit because they played on Wednesday night. We had an extra day to recover from our midweek win and I still thought we lacked a bit of freshness at times.
"I introduced new signing Erik Huseklepp in the last few minutes and he looked very sharp. I'm hoping to take on two or three more players, but it might be through the loan market, rather than permanent transfers.
"You have to take your opportunities in this league because the teams are very closely matched.
"We played some good stuff in the second half, but just lacked that killer finish."
Bristol boss Keith Millen was pleased with the way his side battled to the end.
"I'm proud of my players. They didn't have much time to recover from a tough game at Leicester and there were some tired legs in the second half," he said.
"I was turning to my assistant and asking him which players looked the most tired. It was a job to tell, but we kept going and only one team looked like winning it in the last 10 minutes.
"It was important to us to get our first clean sheet of the season and it's another result to build on after losing our two opening games.
"We looked dangerous on both flanks, but even though we got some decent balls into their box we came up against some very strong defenders.
"I was really pleased with our back four as a unit. It wasn't the personnel I would have picked at the start of the season. But we have overcome injuries and illness which shows the strength of our squad."