Spain, who suffered a shock 3-2 defeat away to Northern Ireland in their previous match, were put to the sword by group leaders Sweden.
The defeat left Aragones's side in fifth place in Group F with three points from three games, one behind Denmark and Northern Ireland and six adrift of Sweden.
It is the first time in 15 years that Spain have lost two qualifying matches in a row. The last time it happened they failed to qualify for the 1992 European championship.
Aragones offered to resign after the Northern Ireland defeat but changed his mind almost immediately. This time he insisted he had no intention of throwing in the towel.
''I feel strong enough to carry on,'' the 68-year-old told reporters. ''I'm not going to make any move to resign. Whether I continue or not will depend on the Federation and the press.
''When you lose two important games things are obviously difficult, but I've spent a long time in football and dealt with situations like this before.'' Angel Maria Villar, the president of the Spanish Football Federation, gave Aragones his backing.
''The whole Federation is behind Luis Aragones,'' Villar told Spanish state television. ''We have full confidence in him.
''He is going to keep working with the national team and we will qualify for Euro 2008.'' The build-up to the Sweden match was dominated by Aragones's decision to drop Real Madrid striker Raul for the first time in 10 years for a reason other than injury and by declarations from out-of-favour winger Joaquin that the national side was ''in chaos''.
But now the debate is centred on criticism of the coach and the Spanish Federation, with sections of the media and fans calling for the resignation of both Aragones and Villar.
''Luis is determined to carry on, but no one believes in him,'' said sports daily AS on its front page. ''Out!'' screamed the headline in El Mundo Deportivo, while Marca declared: ''No one can take any more of this.'' Striker Fernando Torres admitted the defeat was a major blow to Spain's hopes of qualification, but said there was still time to rectify the situation.
''It is a big setback and we can't afford any more slip-ups from now on,'' he told reporters. ''But the positive side is that there is still a long way to go.'' Spain will have home advantage in their next two qualifiers when they play Denmark and Iceland next March.
REUTERS AB PM1349