The game was a dour one for the 8,443 crowd, which included 2,365 from Portsmouth, with neither goalkeeper having to make a save of note.
But Barker felt that was not his concern.
"At times it's not our job to come away and attract other teams' fans," he said. It's our job to grind out results and that's what we've done here.
"Oxford have been a top four or top six team all season, they're good team, so this was a decent result for us.
"I'm pleased with the fact that we've now kept three clean sheets in four, and it's just one defeat in four. If we could carry that on to, say, one defeat in 10, then I think we could say that we've turned the corner.
"I'm extremely pleased with the workrate and the desire of my players. Away from home we did what was necessary
"You have to remember that I inherited a club that had the worst defensive record in the entire Football league. I had to make sure we somehow become more difficult to beat.
"It's not the clean sheet that's the important thing, it's the manner of the clean sheet.
"Probably the best chance for either team fell to us, to Joe Devera. But it was one of those days when any scoring was most likely to come from a set piece, partly because the set piece deliveries were very good, and partly because neither team was managing to create a lot."
Former England defender Nicky Shorey was one of three players to be given their debuts by Barker, and he employed Shorey in a midfield role.
Barker said: "We brought Nicky Shorey in because he can play in more than one position. I was pleased with the job he did.
"More players are likely to come in, possibly this week.
"And the players who were out there looked as though they were playing for their places, because we also have good layers on the bench, and players looking to come back from injury."
With several teams near the bottom of League Two enjoying a successful day, Pompey are now just a point above the relegation zone.