A video from Monday night's clash with Shamrock Rovers at Tallaght Stadium shows a section of Blues fans singing songs including The Billy Boys.
Sinn Féin have raised concerns over the alleged sectarian behaviour.
Oliver McMullan MLA said: "Video footage has emerged which clearly shows a large body of Linfield fans engaging in sectarian chanting and songs. There are also altercations by supporters with members of An Garda and several pitch stewards.
"Given the clarity of the footage there should be no problem in the IFA identifying those involved and sanctioning them for their behaviour. If the IFA are sincere about stamping out sectarianism within Irish soccer they need to show leadership on this issue."
Gardaí confirmed two fans from the Belfast club were arrested for public order offences during the game and later released.
One officer from the Irish police force suffered minor injuries after he was thrown from his horse when a flare was fired in his direction.
Sectarianism has no place in football anywhere on this island or anywhere else and should not be tolerated by either soccer clubs or the IFA
It has been claimed Linfield fans also removed a Tricolour from a flagpole at the stadium and replaced it with a Union flag - although a Tricolour was seen flying alongside the Union flag - after their side lost 4-1.
But Blues fans told UTV they were angry at perceived one-sided policing by gardaí and said home supporters were also involved in singing chants.
Football's governing bodies in both jurisdictions united to condemn sectarianism.
"The Irish FA are aware of the actions of some fans during the Setanta Sports Cup game between Shamrock Rovers and Linfield and unreservedly condemn such acts of inappropriate behaviour in football," a statement from the organisation told UTV.
"We will continue to work hard to promote our Football For All message and the actions of some supporters will not deter us in continuing this campaign.
"As this competition is a cross-border tournament, all matters are dealt with by the Setanta Sports Cup Committee."
The Football Association of Ireland said: "The FAI, with the IFA will continue to work closely with clubs and supporters to eradicate racism and sectarianism which have no place in the game.
"We condemn these incidents which will be dealt with by the North South Setanta Sports Cup committee who run the competition, receive the match reports and handle disciplinary matters."
The return leg of the game is to be played at Windsor Park on Monday.