Fylde twice came back from behind to share the spoils but unhappy manager Dave Challinor issued a stark warning to his players after a tense finish at Kellamergh Park.
Neighbours Chorley were also held by Stamford, meaning Fylde stay top of the Evo-Stik Northern Premier, though one goal conceded is all that separates the Lancashire clubs.
And Challinor pulled no punches, saying: “I don’t think we’ve learned the lessons of the past few weeks. Teams will come here and set up defensively, and hope to keep a clean sheet and get something out of the game. We need to be better than that.
“People aren’t learning, and if they can’t take on board the information we give them, then there comes a point when we have to get people in who do. It’s getting very, very close at the moment.”
Barely five minutes had gone when Harry Winter missed a great double chance to give Fylde the lead. The ball was swung in from the right for Winter to shoot straight at Buxton keeper Andy Warrington before firing the rebound high over the bar.
Two minutes later, Fylde were denied a penalty when the ball was clearly handled by a Buxton defender as he tried to prevent Danny Lloyd getting a shot in.
And when Lloyd saw a free-kick caught by Warrington, Buxton raced upfield and took the lead against the run of play on 13 minutes, Leon Osborne half-volleying home from just inside the box.
It was a very open affair but Fylde began to gain momentum. Adam Sumner, making his 100th appearance for the Coasters, broke and fed Lloyd, whose effort from a very acute angle landed on the roof of the net.
Winter and Matty Blinkhorn both missed chances to equalise but Fylde’s intense pressure paid off in first-half stoppage time, when Lloyd jumped highest at the back post to nod in Mike Barnes’ expert cross.
Both sides knew the next goal would be crucial, and after Derek Niven shot wide it was the visitors who struck again on 57 minutes.
Craig King broke on the left and fed Osborne, whose lay-off gave Lee Morris plenty of time to score unopposed from 12 yards.
Joe Booth came on for his 250th Fylde appearance but his header was comfortably gathered by Warrington.
King remained a danger for Buxton but squandered two great chances in three minutes to give his side a two-goal cushion.
First he tried to lob keeper Ben Hinchliffe but sent the ball into the stand, then he shot wide from the edge of the box.
Challinor made an inspired substitution with 15 minutes to go, bringing on Jack Dorney for Caspar Hughes, and within seconds Dorney had scored Fylde’s second equaliser.
Sumner made another great run to poke to the ball through to Dorney, who was free in the area and slotted home
With 10 minutes to go, Craig Mahon almost marked his Coasters debut with the winner. The loan signing from Chester defied Niven’s efforts to bring him down but fired inches wide.
Neither team could find that all-important third goal and manager Challinor was displeased with his team’s overall performance.
He said: “You have to say it was two points lost, but you can’t afford to give the goals like that away and still expect to win. To have to score three goals to win at home is criminal and the goals we gave away were embarrassing.”
Fylde face a rearranged trip to Barwell on Saturday because scheduled opponents Stamford are in FA Cup action.
AFC Fylde: Hinchliffe, Hankin, Sumner, M. Hughes , Russell, C. Hughes (Dorney 75), Mahon, Winter (Booth 57), Blinkhorn, M. Barnes, Lloyd (Rainford 63): Subs not used: Denson, B. Barnes.