On Saturday, James Brokenshire became the first secretary of state to attend a gaelic football match in Northern Ireland.
It is understood he was in the stadium's control room when the anthem was played.
The Northern Ireland Office said he attended "in the spirit of friendship".
However, A County Armagh Labour MP said Mr Brokenshire had "snubbed" the anthem.
"I think that's quite a regressive step," Conor McGinn told BBC's Good Morning Ulster programme.
"I'm confused and bemused by it and I've asked him to clarify why he did it."
Mr McGinn said he understood Mr Brokenshire arranged it so "he wouldn't be present to take his seat" when the anthem was played before the McKenna Cup final.
"Four years ago Her Majesty The Queen visited Dublin and Croke Park, we've since had a reciprocal visit from the Irish president where both anthems were played with mutual respect, were attended by the taoiseach (Irish prime minister), the prime minister, other ministers.
"So what I want to find out is: Is this a change of protocol and why Mr Brokenshire didn't observe the normal courtesies and protocols around the playing of the national anthem?"
In 2012, then first minister and DUP leader Peter Robinson attended the McKenna Cup final, his first GAA match.
Mr Robinson also took his seat just before the game began after the anthem was played.
In 2011, then sports minister Carál Ní Chuilín became the first senior Sinn Féin member to attend a Northern Ireland international football match. She also did not take her seat until after God Save the Queen was played.
Mr McGinn said he was "not naive" about the feelings of unionist or nationalist politicians, but that Mr Brokenshire is a "UK government minister".
"James Brokenshire should be there as the secretary of state for Northern Ireland, a co-guarantor of the (Good Friday) agreement and someone who is above the fray, in a sense.
"He should observe proper respect and protocols for the Irish national anthem, in the way that I would expect the Irish foreign minister to observe the protocols of the UK national anthem."
A spokesperson for the Northern Ireland Office (NIO) said Mr Brokenshire was "delighted" to attend the match and he "did so in the spirit of friendship".
"Saturday night was about sport, not politics," the spokesperson added.
Speaking about the match on Saturday, Mr Brokenshire said he had received an "absolutely incredible" welcome.
The Secretary of State has been criticised after it emerged he took his seat at a GAA game after the playing of the Irish national anthem.