"[The score] probably slightly flattered us, maybe it should have been 2-1," he said.
The conditions played their part, with a heavy pitch doing neither side any favours.
While Old Blues were good value for their triumph, they only really took control late in the game, and for much of the 90 minutes, the result was in the balance.
Papamoa started stronger and created the first of the chances before the home side hit back, but both efforts were well off target. The next opportunity came from a free kick from Higgins that hit the wall and bounced into keeper Ben Johnstone's hands.
When the first goal came it was from a poor goal kick from Papamoa goalkeeper Ben Pamment that was chested down by Dion Bartosh, who then held it up for Josh Taylor to make a well-placed shot, giving Pamment little chance.
Pamment was nearly caught out by a long-range attempt from a free kick by Hansen, but then made up for his earlier mistake with a great save of a Tom Taylor shot, who hit the final chance of the first half straight at the Papamoa keeper.
Papamoa started the second half more convincingly, with chances falling to Mehdi El Barakat and then Higgins, whose effort drew a great save from Johnstone.
A long-range free kick almost caught Johnstone out, but he managed to tip the ball away. A goalmouth scramble from the ensuing corner saw the ball somehow end up in the back of the net, with sub Brenton Higgs getting the final touch.
Taylor was becoming a threat down Old Blues' right flank and had the chance to restore the lead almost immediately, only to fire over the top. However parity was still short-lived, with Barton getting his head to a cross and sending the ball looping away from Pamment.
Another run into the box by Taylor saw him fouled by Liam Hunt to win a penalty and Luke Wakley stepped up to score from the spot.
"We started slow like we have all season and were a bit sloppy at the back in a few places," said Barton. "I thought they could nick one and they did, but the boys stuck in. I threw myself up there and got my first headed goal in competitive football ever."