Pompey collected their first home triumph since Boxing Day after Ryan Taylor bravely met Daniel Alfei's cross from the right with a looping header in the second half.
Taylor suffered a cut eye in the process of scoring Pompey's winner and left the field with a groin injury eight minutes later before his colleagues defended for their lives in stoppage time to close the game out.
After seeing his men booed off by sections of the crowd at half-time, Barker was delighted with his side's work ethic as a huge victory was greeted with a rapturous roar at the final whistle.
While the game was anything but a classic, Barker claimed his team's battling spirit more than made up for it.
He said: "It was never going to be a pretty football match. The fans were excellent and I think they appreciated the effort and desire to make sure we didn't get beaten.
"Was it entertaining? Not really in terms of technical ability, but it was never going to be. We're talking about the middle of February on a pitch that has had buckets of rain for the last few weeks.
"It was about rolling your sleeves up and showing your desire to win the game. I think these fans appreciated that.
"It's a results-orientated game. I don't think this game was any different to half a dozen of the last ones, other than we won it and people went home happy. But we won't be getting carried away with this one result.
"The players were all fantastic, every one of them. We've kept five clean sheets in 10 and lost two in 10. We're hoping that more mental desire and the ability to see games through will come."