Michael Duignan questioned the amount of time that was added in Tullamore, as Antrim snatched a late draw in the Allianz Hurling League to end the host's league campaign.
The Faithful County looked to be heading for next week's final, also against today's opponents, when they led by six points in second-half stoppage time.
But Saffron goals from Neil McManus and Conor McCann dashed their hopes, consigning them to at least another year in Division 2A.
Referee David Hughes added six minutes of added time, but then played a further two minutes when players suffered injuries.
"We played really well," the Offaly County board Chairman told RTÉ Radio 1's Sunday Sport.
"I thought it was a very, very good performance.
"8 minutes into injury time, there was a minute played in the first-half... strange."
'They were two high balls in that weren't dealt with, and that's the disappointing part.'@Offaly_GAA County Board Chairman Michael Duignan spoke with @JohnKennyMedia after Antrim fought back to draw at Tullamore this afternoon #RTEGAA #GAA pic.twitter.com/71SpM3goRD— RTÉ GAA (@RTEgaa) March 8, 2020
Pushed on whether he was questioning the time that the referee had added on, Duignan said he thought it hadn't been a good day for Hughes.
"I think in fairness the referee, all through, wasn't very good. I thought he was very inconsistent.
"He gave an awful lot of frees against both teams.
"I think he gave six frees against Offaly for throwing the ball. One of them was right in front of us, it was a clear handpass.
"I don't know where he found six minutes in the second-half, and then played another two, but that's hurling."
Offaly needed a win to book a place in next week's decider, but they now face a wait until the summer for their next game.
That will come in the Christy Ring Cup, after relegation from the Joe McDonagh in 2019.
"You look at your Westmeaths, your Laois, your Carlows; they have moved ahead of us," Duignan continued.
"And they're struggling up in the top divisions. So there is a gap developing between the top seven or eight, and the rest.
"We're in the rest at the moment.
"It is a big blow for Offaly. It's a big blow for the county. When you're trying to get up, you need a bit of luck, maybe get a break, get the crowds back, get people behind you.
"We're playing Christy Ring this summer, and that's the height of it, and that's the reality of it.
"We have to get back in there next year. It's 12 months down the line, it's a long time to wait.
"And there's no guarantees next year either."