The Lions cost themselves any chance of jumping Port Adelaide into second place with a demoralising 41-point loss to the fired-up Suns on Saturday.
It was Brisbane's first loss in 10 games against the Suns dating back to 2018.
Midfield general Lachie Neale was shut down by best-on-ground Touk Miller while Noah Anderson pulled the strings for the Suns and Ben King kicked five goals to snuff out Harris Andrews' influence.
The Lions' inability to disrupt the surging Suns drew criticism from retired club great Jonathan Brown, who told Fox Footy they had "been bashed into submission".
They could also be without influential defender Keidean Coleman, who was sent to hospital after an accidental knock to the eye during the loss.
Fagan agreed the Suns appeared the hungrier of the teams but was hesitant to comment on the tactics around Neale's tag that kept him to just 17 disposals.
"It's one of those things you need to look at the tape and reflect on before I answer," he said when asked if they could have handled the Suns' tactics differently.
"The other team were so damn good; you've got to give them a pat on the back and say well done."
Sitting third, Brisbane are two wins clear of GWS in fifth but missed a chance to pressure Port Adelaide, who began the round one win clear in second.
The top two sides earn home-ground advantage on their path to the grand final.
"I've probably have never talked about top two, everybody else talks about top two," Fagan dismissed.
"We're just trying to finish as high on the ladder as we can and to get the double chance (as a top-four side) is the priority.
"I understand the idea you get home finals, but we're not hanging our hat on having home finals to be good enough in September.
"You have to win anywhere at any time in September."
Brisbane's next assignment is a trip west to play Fremantle, who beat Geelong on their home ground earlier on Saturday.
"The competition is so tight, anything can happen," Fagan said.
"You don't want to overreact to a loss. You look at it honestly, see it for what it is and pick yourself up and go again."
