McClean was furious at not being called off the bench during the clash in Astana, which the Republic won 2-1 thanks to late goals from Robbie Keane and Kevin Doyle.
He wrote on Twitter after the game: "Delighted as a fan we got the the win.. Personal level #fuming #f****njoke #embarrassing."
McClean deleted the tweet within 15 minutes, but it had been widely noticed and he returned to Twitter on Saturday morning to issue an apology.
He wrote: "i apologise for my tweet last night, it was stupid, disrespectful and i let my frustration get the better of me which still aint an excuse."
Republic coach Giovanni Trapattoni is aware of McClean's outburst and must now decide what action, if any, to take against the 23-year-old Sunderland player ahead of Tuesday's friendly against Oman at Craven Cottage.
The tweet once again raised questions about Trapattoni's relationship with some of his players.
Last week Darron Gibson informed Trapattoni he would not be joining up with the squad due to his lingering disappointment at spending the European Championship on the bench.
And earlier this summer Kevin Foley refused a call-up to the squad for the Serbia friendly and vowed never to play for Trapattoni again after being overlooked for Euro 2012.
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