Cavan's Padraig Faulkner admitted it was "annoying" that they were unable to break into the Sam Maguire race via the league, though he insists the squad are not dwelling on it as they continue to power through Division 3.
With two games remaining, Mickey Graham's side are effectively guaranteed promotion, having beaten the trio of teams - Westmeath, Down, Offaly - on six points, while boasting a comfortably superior points difference to the latter two.
However, the path to the Sam Maguire competition is blocked off thanks to the unusual draw in Connacht, which has plonked the Division 4 counties (plus New York) on one side of the draw, guaranteeing one of them a slot in the elite race.
"We did address at the start of the year," Faulkner told RTÉ Sport.
"Winning a Division 3 - obviously we haven't won yet or we haven't put our sights at that yet - doesn't guarantee success in reaching the All-Ireland campaign
"It is something that we have to set our sights on, that we have to get to an Ulster final to guarantee success in the All-Ireland campaign.
"It is annoying. We're not dwelling on it. We're just taking each game as it comes. We'll have to set our sights on the league first and then after that, we can look at the championship campaign."
As to the suggestion as to whether the provincial championships could be seeded to militate against such an outcome in the future, Faulkner wouldn't be inclined to agree, acknowledging that rarity of the draw and admitting it affords the counties in question a chance of reaching the All-Ireland series.
"Obviously, statistical probability wouldn't have the counties on the same side (of the draw). It's a great incentive for those teams to go onto a provincial final I don't think I'd take away that from them."
Cavan's league form has been ragged in recent years, even dropping into Division 4 after the Covid shortened 2021 campaign, all the more curious given that it came hot on the heels of their famous Ulster triumph in the winter of 2020.
Prior to the Ulster win, Graham had made plain that championship was his priority. However, with a direct link to the championship established, this attitude appears to have shifted.
"We are looking for consistency, we haven't really seen it in league form over the last few years," Faulkner says.
"We've had high highs and low lows, but we have bounced up, down, up, down, we are just looking for that consistency playing the Division One and Division Two games.
"If somebody had said we'd have won five games on the trot we'd have snatched that straight from someone's hands.
"Winning can become a habit, but at the same time losing can become a habit too. It all depends on your next game. We are in good form and in good spirits too, taking five games in a row we are happy with where we are in the table too."
The 29-year-old Faulkner, who made his senior debut in 2016, is closing in on a century of appearances for the county, currently sitting on 96.
He is quick to point out he is in good company, with a cluster of teammates also closing in one the tonne, crediting the strength and conditioning regime put in place under Graham and co.
"Just looking at the panel we have at the minute, we have myself coming up, Jason McLoughlin is coming up to it very soon too, Killian Clarke, Killian Brady, Gearoid (McKiernan), Ray (Galligan), Marty (Reilly) - a lot of lads have clocked up 100 performances for the county.
"It is a serious achievement, it is a credit to past managers, strength and conditioning coaches, and entire panels that lads are playing for so long and really sticking to it."
Graham, who led Mullinalaghta to an astonishing Leinster title victory in late 2018, is currently in his fifth campaign as Cavan boss.
In his first two seasons, he guided them to successive Ulster finals, including the famous victory in 2020.
"As well as keeping things fresh, he brings consistency too," Faulkner points out.
"This year he has brought in James Burke, who has brought a freshness to the game, a real focus on defending and attacking, he brings a new approach. One of the appointments at the start of Mickey's management was the appointment of Andre Quinn, he has been top class with our strength and conditioning, and overall player development.
"I think Mickey will say himself, he is as only as good as his backroom staff, and he really has that in place over the last few years."
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