Spain coach Inaki Saez regretted his team's inability to finish off Greece after the 1-1 draw that left the sides tied at the top of Group A.
Saez said: "We made our only error in the second half and it cost us a win.
"We had the game within our grasp. We attacked well but we just were not able to finish off some promising moves.
"We risked too little. Anything could have happened, but this result is not good for us. We will be tense for the rest of the week."
To qualify, Spain now need a result from their final match against arch-rivals Portugal on Sunday, while Greece are fancied to go through with just a match against the weak Russians remaining.
Fernando Morientes gave Spain the lead on Wednesday, and despite applying relentless pressure following Angelos Charisteas' equaliser Spain could not score again.
"We made errors in the middle period of the game and our shots didn't go where they should have," Saez added.
"We played very well in the first half, but I accept Greece came back at us and caught us out on the break.
"I know we missed chances, but I do not blame individuals, everybody contributes and I will not point the finger at any one player."
Substitute Juan Carlo Valeron added: "We will have to go for it against Portugal.
"What's important to me is the result. Greece were a hard, rocky team."
Defender Carles Puyol, who could miss the Portugal showdown with a knee injury, admitted they were pushed hard by the Greeks.
"It was a very tough game for us," said Puyol. "We tried to win. We attacked a lot and we had some chances but we could not score a second goal.
"It is going to be even tougher against Portugal."