Jennison Myrie-Williams should have put Vale ahead in the first half before goalkeeper Chris Neal saved twice from Barnet's Andy Yiadom before the break.
The Vale stopper then denied John Oster and, despite a late rally, neither Doug Loft nor Tom Pope could beat Graham Stack as the game finished goalless.
Player/manager Davids said: "If you have a display of football like this against the top of the league than you can't ask for more. We played such great football and it's getting better and better. Hopefully the three points will come. Technically we were great and in attack we were great. We just weren't clinical enough.
"When you play against Port Vale it's hard because they're a team in form. You don't know what to expect. We could've had three points.
"We lack that clinical finish. We can play well but in the final third we have to score the goals. If you play well and it's 1-0 or 2-0 then you play more relaxed.
"Every game is a final for us and with Barnet you don't know what to expect. But I hope we can continue playing the good football we're playing.
"We're disappointed we've only picked up one point in our last three games, it's a big blow."
And Vale boss Micky Adams openly admitted his table-topping side were second best to Barnet.
"It was a good point based on our performance. Barnet were fantastic, they were better than us," said Adams.