The inquest also heard how Mr McCormick, 51, stayed with Mr Bird, comforting him and making contact with his family in Australia to let them know what was going on.
Mr McCormick told the Herald he was left feeling numb when Mr Bird died from "massive crush injuries".
"In the end, it was a certain amount of relief - I have to be honest. By that stage Carey was just exhausted. In the end he was struggling to breathe."
Mr McCormick arrived at the collapsed PGC building soon after the deadly 6.3 magnitude quake struck Christchurch, but says he is still not quite sure why he went there.
He joined with others trying to help free people, and helped some to safety from the debris before he came across Mr Bird pinned by a section of wall.
"He was quite badly trapped. He was quite buried ... with debris and what have you. You couldn't see his right arm and right leg."
Mr McCormick, an engineer, used a power saw to cut away a metal beam lying across Mr Bird's head. Medics did what they could to keep Mr Bird comfortable, setting up a drip and providing pain relief.
The task of freeing him always seemed a hopeless one, Mr McCormick said. Mr Bird's body was not freed from the debris until two days later.
Although struggling with cellphone reception, Mr McCormick managed to get through to Mr Bird's family to explain what was happening. He passed messages back and forth through the afternoon.
Eventually it fell to him to call Mr Bird's wife, Jan, and tell her that her husband had died.
"You sort of think 'well, if I hadn't contacted her ... she might not even know'. In a way you sort of question 'would that be a better situation?' ... Because now she is absolutely distraught."
Mr McCormick said he had no regrets that he was the one at Mr Bird's side.
He had since spoken at Mr Bird's funeral and spent time with his family.
"While you come away with a feeling that 'I have been no use at all - I wasn't able to help him' ... [it's worthwhile] knowing what it meant to the family that there was actually someone there [with Mr Bird]."
The quake inquests before coroner Gordon Matenga continue today.