There was a deathly hush in the bar where officials gathered to wait for the result of the International Olympic Committee head-to-head vote that eliminated the Spanish capital following a first-round tie with Istanbul.
The third bidder, Tokyo, was later awarded the Games.
“We believe the result bears no relation to the way (our presentation) was made. A decision like that is based on other criteria,” Spain’s Education Minister Jose Ignacio Wert told reporters.
“Everyone who attended the presentations of the three rival cities today can be in no doubt Madrid’s was the best.”
Some members of the large Spanish contingent were in tears when they emerged on the streets of the redeveloped port area of the Argentine capital on a grey, rainy afternoon.
Madrid, bidding for the third successive time, was confident of success after narrowly missing out on the 2012 and 2016 Games.
Fencer Jose Luis Pirri echoed Wert’s comments and suggested tactical voting had eliminated the Spanish capital.
“We expected to be in the final with Tokyo but it’s obvious they didn’t want us in the final because Madrid would have been very strong,” said Pirri.
“It’s a strange decision. Madrid has deserved to hold the Games for a long time and on top of that we are out in the first round, it’s quite absurd.”
NBA basketball player and Olympic silver medal winner Pau Gasol, a figurehead of the Madrid bid, could not hide his disappointment.
“There are factors we don’t control, that only (the IOC members) know about. It’s a shame because we were confident and had a good feeling,” Gasol said.
“I don’t think our work has been duly recognised in this instance.”
Enrique Cerezo, president of top football club Atletico Madrid, said: “I think it’s unfair Madrid should have been eliminated at the first turn. It looks to me like the system is very badly designed.”
(Additional reporting by Damian Perez; editing by Tony Jimenez)