Even if the Lions beat Collingwood in the final round next week, they will have to travel either to Sydney to face the second-placed Swans, or Perth to play minor premiers the Fremantle Dockers.
"There's a team called Fremantle that's going to be very hard to beat, given the home-ground advantage they're going to get until they get to a grand final," Fagan said.
Fagan was coaching a club-record 238th game, surpassing triple-premiership coach Leigh Matthews. He has a real chance of joining Matthews in that ultra-elite club in September.
Asked about his achievement after the game, Fagan said the club had made him feel special during the week, before deflecting the attention.
"Enough about me. Ask me some questions about the game," he said, laughing.
Fagan said he was relieved that the club's final-four destiny remained in its own hands.
After a shaky first half to the season, the Lions have won nine of their last 10 games.
"All you do every year is try and give ourselves a chance, and we've done a good job to give ourselves that," Fagan said.
The Suns fought valiantly to limit the Lions for three quarters, before the home side finally broke free, running away with the game in the last term for a 14.11 (95) to 6.17 (53) victory.
Terrible finishing in front of goal and two critical errors in the third quarter sabotaged the Suns' efforts.
First, stopper Sam Collins shanked a kick out of defence that was pounced on by Charlie Cameron, leading directly to a goal by Collins' opponent, Logan Morris.
A few minutes later, Beau Addinsall gave away a silly 50-metre penalty to Dayne Zorko at half-back. With no one on the mark, Zorko waltzed through middle and rifled the ball through an unguarded goal square.
The Lions had most of the dominant players on the ground, with the Ashcroft brothers Will and Levi having 57 disposals between them, Zorko finishing with 25 possessions, and Morris continuing his hot run of form with four goals.
Will Ashcroft - son of Lions legend and former Suns administrator Marcus - finished with his second medal struck in his father's name.
For the Suns, Matt Rowell dug in without hitting the heights of his efforts against GWS last week, while Ned Moyle also competed manfully in the ruck with 41 hit-outs.
But effort wasn't the issue for the Suns. Collectively, they won many key indicators on the stats sheet - inside-50 entries, centre clearances and contested possessions were all in their favour.
It was their failure to execute and a lack of composure at key moments that undid them.
"You know what they won? Polish," Suns coach Damien Hardwick said.
"I thought we had really good opportunities to score; we just made it look hard, and they're a cleaner and more polished side at the moment.
"We gave them four goals that were just giveaways, just through blatant errors, not necessarily Brisbane's good play.
"So they're things we can rectify and get better at. We just weren't clean enough at various stages."
The Suns also experimented again with playing Christian Petracca in attack for minimal return, the former Demon finishing with just 12 disposals.
Hardwick took responsibility for Petracca's downturn in form.
"I've got to find how I can best use him, and it's up to me to figure it out," he said.
"His legacy to me is to help change the fortunes of the Gold Coast Suns, and he's pulling his part in that.
"I think I've got to get better at utilising him to his strengths. I haven't found that right lever yet."
