Bunn, who qualifies to play for the Republic through his father and grandmother, has pledged his international allegiance to Ireland and was tipped to earn his first call-up to the national team for the two recent World Cup qualifiers after impressing for Norwich.
The 28-year-old has kept four clean sheets in his last nine games for Norwich and his performances have been earning rave reviews at Carrow Road.
However, Republic boss Giovanni Trapattoni decided to overlook Bunn despite his lack of options in the goalkeeping department.
What made Bunn's omission all the more surprising was the fact that he is the only available keeper currently playing regularly in the Premier League.
With Keiren Westwood finding himself down the pecking order at Sunderland, Trapattoni decided to plump for veteran keeper David Forde with the Millwall man becoming the oldest player to make his competitive debut for Ireland in the game against Sweden.
Bunn was disappointed not be included in the squad for the Sweden and Austria World Cup qualifiers, but is ready to continue to fight his way into Trapattoni's plans.
"It was disappointing not to make the squad for the last two games, but all I can do is continue to do my best for Norwich and hope I get a call-up next time," Bunn told Sky Sports.