The Minstermen went ahead in the 35th minute when Luke O'Neill's shot from 25 yards zipped inside the right-hand post. They scored again after 61 minutes when Ryan Jarvis flicked in a corner.
But the Spireites hit back three minutes later when Gary Roberts was tripped by Danny Parslow and Armand Gnanduillet fired the resulting penalty into the bottom left corner of the net.
The big striker then crossed for substitute Jay O'Shea to equalise in the 76th minute, but Worthington was still able to reflect on a decent night's work.
"At 2-0 up you want to go on and win the game but you know Chesterfield are going to come at you and you have to deal with that," said Worthington. "I've got to say I was absolutely delighted with the York players.
"They battled and fought and scrapped and a point here is a very good result, make no mistake about that. We said at half-time there was going to be an onslaught in the second half and sure enough there was.
"For a large part of the time we dealt with it. They got two goals and I thought the penalty the referee gave was soft, although the one after that was probably more of a penalty in fairness.
"But you take the rough with the smooth and overall the performance and the energy we put into the game was fantastic and when we do that on a regular basis we are a decent side."