A potential finalist may now have to play four games in 11 days after frozen pitches meant Armagh v Derry (Athletic Grounds), Monaghan v Donegal (Clones) and Down v UU (Burren) did not go ahead.
“It’s far from ideal but it was the right call, you have to look after the players first,” said the Armagh manager.
“It is going to be tough now because it tightens things up a bit. Whoever gets through to the semi-finals is going to have to play three games in seven days.
“More than likely it’s going to one of us (or Derry), though it could be Jordanstown, you don’t know, but for whichever team goes through to the semis has three games in seven days, which is a big ask.”
The postponed games will be played this weekend, which pushes the semi-finals back until January 17, just three days before the final on the January 20.
It leaves the Ulster Council with no further wriggle room for rescheduling games before the start of the Allianz League.
“Both goalmouths (at the Athletic Grounds) were frozen and player safety comes first,” insisted Ulster Council spokesman Michael Geoghegan.
“We will meet on Monday to decide dates and venues for the refixtures.”
Some of the games were called off quite late, with the Armagh v Derry throw-in first delayed from 2pm to 2.30pm before finally being postponed around 1.45pm.
McGeeney was relaxed about the situation.
“No, it was the right call, it’s easy for us because we’re at home but it’s a long journey for Derry to come here, two and a half hours.
“They had to give the game every chance to go ahead.
“It’s quite difficult to try to give fellas a run out and then pull the rug from underneath them, but hopefully as the years go on in the GAA, people will just get better organised and there’ll be other pitches.”
In a clear reference to Tyrone’s game against Antrim taking place in the Athletic Grounds last Wednesday night due a waterlogged pitch in Omagh, McGeeney added: “Us having the game here in midweek didn’t help.”
Asked what he thought about Tyrone playing ‘home’ games in Armagh, he smiled: “no comment!”
Meanwhile, a goal from Omagh St Enda’s defender Ciaran McLaughlin on his debut gave Tyrone a 1-16 to 1-11 win over St Mary’s in Coalisland.
The Red Hands are all but through to the semi-finals as they chase a seventh title in a row.
Sigerson Cup holders St Mary’s scored the first three points before McLaughlin’s 22nd-minute goal.
Jarlath Og Burns replied for the students who trailed 1-7 to 1-5 at half-time.
Peter Harte, Tiernan McCann, Mattie Donnelly, and Ronan O’Neill all tagged on second-half points.
Seamus Quigley nailed a late match-winning penalty on his comeback with Fermanagh.
New boss Rory Gallagher has lured the enigmatic Roslea full-forward back into the fray and he came on in the first half in Brewster Park, before converting a late penalty in the 1-10 to 1-9 win over Queen’s University.
The students led 1-4 to 0-6 at the break following Niall Keenan’s early goal but Jones brothers Conal and Ryan nailed 0-5 between them to get Fermanagh going.
Quigley’s penalty four minutes from time gave the Erne men a second win in the competition.
Meanwhile, Antrim recorded their first win under new manager Lenny Harbinson in beating Cavan 4-11 to 2-13 in Belfast.
The game was played on a 4G surface in Belfast and the visitors started brightly with Bryan Magee’s early goal.
The saffrons hit back with Paddy McBride and Conor Murray goals to lead by three points at the break.
Murray added a second goal in the second with Ryan Murray also hitting the net, with Niall McKiernan landing a late consolation goal for Cavan.