A seventh-minute strike from on-loan midfielder Joe Edwards fired Yeovil to within four points of sixth place - heaping further misery on the beleaguered Pools who are now 14 league games without a win.
Barron said: "I thought we started a little slow and conceded a goal which we should have stopped, but after that we were comfortable.
"We kept the ball well in the first half without creating many chances, but in the second half we had numerous chances to score but couldn't get that goal. If we did get it then I think we would have gone on to win the game.
"I thought we played really well in the second half. That's the unfortunate thing because I don't think the players or the fans deserved to go home with nothing to shout about.
"We can't ask anymore from the players. Over the coming weeks if they play like that and with a bit of luck, I am sure they will pick up some wins. If we are getting played off the park and heavily beaten every week then it would be tough, but here we played well. The boys are looking forward to the next game."