Mrs Foster said she was aware of the significance of her appearance at a game synonymous with the nationalist tradition. DUP ministers have attended GAA games before but none as high profile as the Ulster Final and none in the Irish Republic.
Mrs Foster stood as the Irish national anthem Amhran na bhFiann was played before the throw in and then took her seat only a few away from Sinn Fein’s Stormont leader Michelle O’Neill.
“I do realise that there might be some people who may be uncomfortable with me being here,” Mrs Foster said.
“But let me say this – I am a leader of a political party that wants to have a shared society in Northern Ireland and to do that you have to take steps forward and to do that we have to build a respect and tolerance and that’s what I want to do,” she said.
In an apparent reference to Sinn Fein, she added: “I hope that others take the chance to step forward as well and to understand and appreciate and tolerate another culture perhaps that isn’t theirs.”
Mrs Foster’s hopes of a victory for her home county were dashed, however, with Fermanagh suffering a heavy defeat.
Her appearance came ahead of another significant step next week when she will attend an LGBT event at Stormont.
The DUP has been much criticised by gay rights activists for its resistance to same-sex marriage in Northern Ireland.
Mrs Foster arrived amid a tight security presence to be greeted by Irish culture minister Heather Humphreys.
Fermanagh fans who witnessed her arrival clapped as the DUP leader entered the stadium, with some shouting light-hearted comments of “Go on you girl” and “Come on Arlene”.
The was another positive reception when she briefly walked to the edge of the playing surface to field media questions before walking up the steps to take her seat in the main stand ahead of the game.
She shook hands with Mrs O’Neill, who was sitting just behind her, and the Irish Government’s chief whip and Donegal TD Joe McHugh.
Mrs Foster and party colleague Christopher Stalford then stood with the rest of the sell-out crowd as the Irish national anthem was played.
High-profile Fermanagh born priest Brian D’Arcy said he was “absolutely delighted” at Mrs Foster’s attendance.
“It’s a big step for her and we appreciate that and Fermanagh people will definitely appreciate that,” he told the Press Association.
He said a tweet sent by the DUP leader welcoming the team’s semi-final victory over Monaghan had “broken the ice”.
“If you make the first step and you put the hand out, a lot of people will shake it,” he said.
He added: “Arlene doing this is showing herself to be not just a leader of a political party but actually a politician and we have remarkably few of those – so the more the better.”
Councillor Howard Thornton, the Ulster Unionist chairman of Fermanagh and Omagh Council also attended Sunday’s final in Clones.
Mrs O’Neill also welcomed Mrs Foster’s attendance.
“I along with other Sinn Fein leaders met recently with Prince Charles in order to demonstrate our desire to reach out and respect those across our community of a unionist and British identity,” she said.
“We recognise the important significance of Arlene Foster as DUP leader attending today’s Ulster final and acknowledge and very much welcome her decision to do so.
“She has encouraged others to step forward as well to understand, appreciate and respect another culture perhaps that isn’t theirs in the context of building an inclusive society.
“There is an onus on all in political leadership to build on these recent initiatives and do more together if we want to be successful in bringing about a society underpinned by inclusion.”
Mr McHugh sat beside the DUP leader during the game.
“Arlene Foster showed a real interest in the rules of Gaelic football and several times she asked me about some of the Irish words that you can see and hear on and around a GAA pitch,” he said.
“She really was pleasant company for the Ulster final and I know it’s not simple for her to be there either.”
Leader of the hardline Traditional Unionist Voice party Jim Allister criticised the move as “folly”.
“While at one level Arlene Foster’s attendance on a Sunday afternoon at a GAA match is gesture politics, at another level it is much more,” he said.
“It is patently, along with her planned embracing of LGBT interests later this week, part of a choreographed and Sinn Fein-placating agenda to pave the way for renewed talks aimed at getting back into power in the failed institutions at Stormont.
“Today and Thursday’s moves, though they will cause unease at grassroots level in the DUP, are also designed to signal to any in her party still holding to traditional values that they will be steamrolled in the rush back to government with IRA/Sinn Fein.”