The Bees won a dramatic last game at their Underhill ground on Saturday, with Jake Hyde scoring the decisive goal against Wycombe nine minutes from time.
But they almost threw victory away in the dying seconds when Tom Flanagan fouled Wycombe midfielder Bruno Andrade in the box, only for Graham Stack to save Joel Grant's penalty.
It means Barnet head to Northampton on Saturday a point outside the drop zone and with their destiny in their own hands.
But Davids said: "There is still a major job to complete.
"We have improved but if we make another mistake at Northampton then they will make us pay for it."