Hibs fought back from a goal down to lead 2-1 when Ricardo Vaz Te slotted home with ten minutes remaining but Stephen Elliott volleyed home three minutes later to deny the home side their first derby win since May 2009.
Calderwood said his team played well but failed to do their job at the most crucial moment which disappointed him.
"We were certainly punished for not doing our jobs," said Calderwood.
"I'm happy enough with how we created the chances and how we played in the second half but we didn't get through the big moment.
"We didn't do our job at the big moment and that was the reason they got the excellent second goal. It was a great response by them.
"But we had just lifted the place, we had given the fans everything they had hoped for and we snatched it back from ourselves."