The Coasters were 3-1 up with two minutes to go but late wonder strikes from Jake Cassidy and Devante Rodney gave struggling Pools a point.
The result means Challinor’s men are now four points adrift of the play-off places ahead of Saturday’s trip to Dagenham & Redbridge.
The boss was critical of his side for not seeing out the game and says it was something he had warned them about.
Challinor told BBC Lancashire Sport: “We got ourselves into a winning position and you can look at it two ways. They will think two worldies have got them a point but from my perspective, it’s disappointing.
“You’ve got to make good decisions and we made ones that put ourselves under pressure like giving away silly free-kicks.
“It’s not another win chalked off and now we’ve got a week ahead of us with some players on international duty.
“We spoke a little bit about naivety before the game and it’s come back to bite us. We’ve got to learn from it. We’ve still got eight games to go and we’ll do our damnedest to win them all.”
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