"I'm not going to resign, but they (the Spanish Football Federation) can take whatever measures they want to," Aragones was quoted as saying by AS newspaper after the game.
However, the veteran coach did admit the defeat was his fault.
"The main responsibility lies with the coach, I didn't adopt the right tactics," he said.
Spain squandered their lead twice to fall 3-2 to underdogs Northern Ireland, courtesy of a David Healy hat-trick.
"Spain are a better side than our opponents, but they have dealt us a severe blow that has made qualification for Euro 2008 more difficult."
Spain, who won their opening game against Liechtenstein 4-0, are currently in fifth spot in their Group F of the qualifiers, only three points behind leaders Sweden.
Aragones, who is currently working without a contract, said he wasn't planning on leaving the Matadors.
"I'm not thinking about giving up the post. I'm happy in the job and keen to continue, just as I was when I decided to continue after the World Cup."
Spanish Football Federation (RFEF) president Angel Maria Villar said there was no intention of letting Aragones go.
"We don't want him to resign. He has all of our support and we are convinced that we will qualify for Euro 2008," Villar was quoted as saying by UEFA's official website.