Zamora skied a 47th-minute effort from six yards with the goal at his mercy after Clint Dempsey's initial effort had been parried into his path by Shay Given.
It was a miss destined to go down in bloopers compilations and looked to have swung the game in City's favour as Joleon Lescott and Martin Petrov swept Mark Hughes' men ahead.
But the lively Zamora played a full part in his side's improbable recovery with Damien Duff and Dempsey quickly responding with the goals which gave the Cottagers a deserved point.
Hodgson called the miss "horrific" and added: "Unfortunately people who watch on the TV will see the miss and they won't see the 96 minutes and 45 seconds in which he was absolutely magnificent.
"It should have been seen as the crowning moment of a great performance but instead it is going to be seen as a glaring miss and a blot on his copybook which is sad for him. But if you want a good example of the character and resilience of this team and its ability to bounce back, Bobby's performance in the last 30 minutes shows that."