McRae's Magpies led by 21 points at third-quarter time at the SCG on Friday night but were overrun by a surging Swans unit.
The league leaders slammed five unanswered goals in the final, condemning the visitors to a 12.14 (86) to 13.11 (89) to 12.14 (86) loss.
Key forward Dan McStay had an opportunity to slot the match-winner after collecting the ball 65 metres out from goal when Sydney defender Tom McCartin seemingly walked over the mark.
With less than a minute on the clock, the in-zone umpire did not pay a 50-metre penalty against McCartin.
"I reckon if it was at the MCG it would have been paid," McRae said. "There's definitely an advantage with a home ground. I thought it was a 50-metre penalty to letter the law.
Collingwood coach Craig McRae was unhappy at a number of umpiring calls in Sydney. (Morgan Hancock/AAP PHOTOS)
"I'm sure the AFL will come out and say it's a free kick or a 50-metre penalty.
"There were a lot of deliberates tonight, too. That was a bit of a circus so I'm sure they'll come out and justify that too. The umpires don't always get it right. That's fair."
Collingwood, who sit 11th on the ladder, are unlikely to make the top eight.
The reigning premiers must defeat flag favourites Brisbane and 12th-placed Melbourne but other results will need to fall their way.
"I'm sure our fans at home are hurting and we're no different. We're human," McRae said. "We have emotions to attach to this. It means a lot to a lot of people.
"It doesn't feel comfortable right now sitting in this chair because there's a lot at stake in these games."
McRae then added he was "wrestling" with blame after the loss.
"We've openly talked about what winning looks like and behaviours like that and then losing behaviours," he said.
"I think blame is a real losing behaviour so I'm wrestling with that at the moment. Wrestling with trying to blame others or blame umpires or blame whatever, because that's really difficult when you lose.
"Maybe there are consequences at the end that may cost us. Time will tell on that. For most part of the night, we did a lot right and maybe that's what's hurting us the most."
The Magpies return home to take on Melbourne at the MCG as the away team.
"We'll just meet back earlier in the week and get on with it," McRae said. "We can't control what others are doing. You can only control your own destiny."
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