It's just two years since the Na Fianna club man raised the Sam Maguire at HQ for the very first time in the Ulster county's history, but this is a team burning to confirm their greatness with a second All-Ireland title.
"Everyone talked about what a good year we had last year but at the end of the year we had nothing," said the Armagh skipper.
"This is something, but at the end of the day it's not what we want. We want to go on to bigger things, we want that second All-Ireland title. We just have to get in the queue, there's a lot of teams that want it just as much and it'll probably come down on the day to who wants it that bit more than anybody else."
Hunger doesn't seem to be an issue for this side, despite the fact many of them have been on the road since their first big year in 1999 and even before that. Armagh now find themselves as newly-installed joint favourites for Sam alongside Kerry, but as McGeeney knows, their latest display has now made them marked men. "Once that game is over, people are always going to look at that game, try to analyse it bit by bit and see how to stop us the next day, whether they come through the provincial system or through the back door.
"Look at the teams that are going to come through, you're going to have Limerick or Kerry, Galway or Tyrone, Cork, some of the top teams in the country. If I could pick a winner out of that I'd be a rich man."
So good was Armagh's display that it's hard to pinpoint any player or specific area that stood out over another. Just like manager Joe Kernan did after the game, though, McGeeney singled out some of the forwards who have been the target for some criticism in the past few years.
"It was just one of those days when everybody did their bit. It was an all-round team performance. Diarmuid Marsden was brilliant coming into the second half.
Steven (McDonnell) was well marshalled at times but still managed to get in a couple of scores."
Armagh's style of play in defence in particular has had its share of critics, but McGeeney is sick and tired of hearing moans about blanket defence and forwards tackling like tigers.
"That's part of the game. Football isn't just a case of getting the ball and kicking it over the bar and then you stop. That would be just the same as giving it back to them. It's funny how people go on about blanket defence. When you don't have the ball what do (your forwards) do?
"You have to go and tackle them. If they're running you have to tackle them. You don't just say that once their half-backs have crossed the midway line we'll leave them because that's not our job. You follow your man and maybe then it becomes a blanket defence."
If the criticisms have been annoying then that's nothing to the frustration McGeeney has to endure this past few months with a calf injury that limited him to only 15 minutes against Cavan since the end of the league.
"It was frustrating alright, it was one of my worst periods ever but you have to keep the head down. It's not the Kieran McGeeney show or it's not the Diarmuid Marsden show. The team plays just as well without you and that's a great thing for humility.
"I was lucky the last time that Andy McCann hurt his hand and that let me in because, as far as I'm concerned, Andy McCann is a class act and he's never let us down out on that pitch.
"It was a tough call on Joe because it was a tough couple of weeks and I was just coming back from injury but I've no doubt Andy will be pushing hard for the next one."