The Auckland-based side produced arguably the worst performance in their Super Rugby history, conceding six second-half tries after leading 21-14 at the break.
It has been a stop-start season for the Blues as consistency has been their major problem with the side unable to put together a sustained winning run.
Winning under 50 percent of their games (7 from 15), the Blues were by far the worst-performing New Zealand franchise and the only Kiwi outfit not to make the playoffs.
The next worst-performing Kiwi side, in the form of the Highlanders, won 10 of their 14 games, three more than the Blues which shows the gulf in class between them and their other compatriots.
To be fair to Umaga's men, they have shown glimpses of promise, such as in the 22-21 victory over the British and Irish Lions last month.
However, the season-ending meltdown against the Sunwolves in Tokyo, appears to have been the last straw for a large proportion of fed-up Blues fans who are now calling for Umaga's head.
But skipper Parsons believes the blame cannot lie solely at Umaga's door and that the players have to take responsibility as well.
"I've had so many coaches over my career and, unfortunately I feel like the same problems are still there, so I don't think everything can fall to the coaches," Parsons told Radio Sport.
"It's an easy fix, because it's one man to get rid of, but I have full belief in Tana. We clearly have to make some changes - we're just not getting the results - but he is a passionate Blues man and he's in that building 24/7, trying to make us better.
"The first thing he said to us after the game was he apologised for not being good enough to get us ready for this week. He takes ownership and is a man about it, and I think that's a great man to follow."
Parsons went on to say that the Blues showed a distinct lack of hunger and were guilty of complacency.
"It's a big learning curve for some of our young men," Parsons said.
"They need to realise it doesn't matter what team you come up against, if you think you're going to just turn up and play and win, that doesn't happen at this level.
"I hope they learn and never have to experience that again. If there's one silver lining, it's that there is no false sense of security for us, going into 2018, about where we sit and the adjustments we need to make.
"I've always said that our biggest growth area is consistency and the only way we can get that is when our players prepare on a consistent basis to get those consistent results.
Parsons said the players were so gutted they were dreading flying back to Auckland where their loyal fans would inevitably be waiting for them.
"It's genuinely gutting.
"I make no excuses, we needed to be better than that and we weren't. That is a real-life example that we can use as leaders, as coaches, of what will happen if you switch off ... we were embarrassed, we still are embarrassed.
"The boys were at the airport, wishing they could fly somewhere else, because we knew what we were coming back to and we knew how much we had let people down.
"We have such loyal fans - there were people at the
airport to greet us - and we're so grateful for that support."