Elliot Benyon put the hosts in front before substitute Jake Hyde equalised with his first touch. Goals from Billy Bodin and Brian Saah sealed all three points for the Gulls before Hyde added a consolation goal late on.
The Bees now sit 23rd in the League Two table with just two games left to play.
Davids said: "It's always very frustrating to concede goals from set-pieces, especially as we did it just after we had got back to 1-1.
"We have to show real character to get out of the relegation zone.
"Teams have come from a long way behind to escape, and we must do that now."
He added: "The Barnet fans will be vital when we play Wycombe on Saturday."
Two-goal Hyde said: "Even though I scored twice, they count for nothing because we've lost.
"We are in a dogfight, and we need to win both our last two games, but we've got enough in our dressing room to stay up."