"We are disappointed, but you have to accept defeat," said the secretary of state for sport, Jaime Lissavetzky, following Russia's win in Thursday's vote.
"We must congratulate the winner," he said, adding: "We can still have our revenge by bringing back the World Cup in 2018 from Russia to Spain."
Spain hosted the World Cup in 1982 and are the reigning champions after winning the tournament in South Africa in July.
Spain's coach, Vicente del Bosque, congratulated both Russia and Qatar, which was named to host the 2022 tournament, but said "we had all conditions to organise the World Cup," mentioning the sporting facilities in a "modern country" that has a "passion" for football.
"We also have a good league, we have extraordinary players, including our own, who are world champions," he said.
"But, hey, I suppose that (members of FIFA's executive committee) had different criteria from us," he said.
He said these criteria might be "to expand football to other regions, and, well, they (Russia and Qatar) are countries with economic weight."
The head of the joint Spain-Portugal bid, Miguel Angel Lopez, also said the decision appeared to have been based on FIFA's desire to stage the World Cup in nations where it has never been held before.
"Football is looking for new horizons. That is very good and it is very honourable that it is not always the same continents," he told Spanish journalists in Zurich after the decision was announced.
"The executive committee felt it would be best to go to a region where there has never been a World Cup and thinks this is an opportunity for modernisation. FIFA thought it was best to promote football in other latitudes."
But he also complained that the decision appeared not to have been based on the technical reports which were submitted by the candidate countries.