Striker Jake Hyde netted the winner from a Luke Gambin cross in the 81st minute as Barnet brought to a close 106 years of playing at the famous old ground.
The fairytale ending was on the verge of turning into a nightmare when Tom Flanagan fouled Wycombe midfielder Bruno Andrade in the box in injury time.
But Joel Grant's spot kick was pushed wide by Graham Stack with Barnet moving out of the League Two drop zone with a one-point cushion ahead of their final fixture at Northampton.
And Davids wants the fighting qualities shown by his players to grind out a win against Wycombe to be displayed again when they travel to Sixfields to meet the Cobblers.
"We created enough chances to win the game but we had to really battle to get it," he said. "We came in with a mission and we started with our foot on the gas.
"We really went for it from the first minute right up until the last minute. Wycombe couldn't deal with our pressure - we were pushing right up inside their half.
"If you believe from the first minute to the last that you will win, most of the time you will get that chance. And with Jake, if you miss a lot chances, the laws of football suggest that you will eventually be able to score.
"Conceding that penalty at the end sums up the season for us. Every game we play there is an error and we just keep doing it.
"Northampton also play very directly and they have two very good strikers so it will be another tough battle for us."