The Scots had never been behind over the two legs of the play-offs, yet found themselves eliminated in the 122nd minute of the return in Las Rosas, near Madrid, despite being the far superior side.
Three minutes earlier it had looked as if Scotland would go through on away goals when captain Gemma Fay saved a penalty from Veronica Boquete. Then the same player found the net, via a deflection, in the second minute of stoppage time.
Earlier, the teams had gone into extra time when the match finished 1-1 after 90 minutes.
"Where did the extra minute come from?" asked a furious Signeul. It was a fair question, as there was no obvious reason why German ref Bibana Steinhaus had extended the second period of extra time for so long.
"We have been so unlucky in these two games and Spain have been very lucky. We deserve to be in Sweden, not them.
"We have a very good young team. It is unfair that Spain are going there and not us because we were worth it more than them.
"I told the players I am very proud of them and they did fantastically in this campaign. We don't have many older players, but the ones we have I've told not to retire because the next thing is to qualify for the World Cup in Canada.
"The team is so young, with an average age of 24. They are just going to get better and better, I am very proud of every one of them.
"I am so sad, because I didn't want this for myself or for Scotland – I wanted this for them."
Emma Mitchell put Scotland ahead in the second half – a lead the visitors thoroughly deserved.
Spain equalised through Adriana, who also got the Spanish goal at Hampden, to send the tie into extra time.
It looked as if Scotland would qualify for their first major finals when Kim Little fired her side ahead in the first period.
Silvia Meseguer gave Spain hope when she equalised for the second time on the night, and the third in the tie.
When Fay pulled off a terrific save from Boquete's penalty – she had saved one from Adriana at Hampden as well – it seemed as if the Scots would go through.
But then Steinhaus added two extra minutes, Boquete scored with the last kick of the match.