The Green and White Army's hopes of qualifying for the tournament were put to an end by Switzerland on Sunday evening, as they were held to a goalless draw in Basel following on from Thursday's controversial first-leg defeat.
O'Neill has been tipped to step aside now that his side's World Cup campaign has come to an end, with a number of Premier League and Championship sides likely to be interested in his services.
Asked after the match whether he intended to quit, however, the 48-year-old told Sky Sports News: "I'm not giving it any thought. I don't think it's a reasonable question to ask me to be fair.
"My focus is with the players in the dressing room. They couldn't have given any more. What they gave for me, what they gave for each other, what they gave for their country was phenomenal."
Northern Ireland, who finished second to world champions Germany in their qualifying group, do not return to action until next March at the earliest.