The world No. 1, who was seeking a record fifth consecutive title, crashed to a fourth-round 6-2, 6-7 (2), 6-4, 7-6 (2) defeat to the Swedish 23rd seed.
Emilio Sanchez Vicario, who captained Spain's Davis Cup team to victory over Argentina last year, watched the game on television from Barcelona.
"Soderling played very well, and that is tennis sometimes," he said. "In tennis there are times when one player gets into the game and the other player can't find his rhythm. When Nadal went so far behind in the second tiebreak there was no way back.
"I think he had been having problems with the length of his shots all week and he suffered for this," he said. "He couldn't get back into it. I don't think it was down to tiredness. He'd won a lot of games recently and was quite fresh."
Spanish former Wimbledon champion Manuel Santana wrote in sports daily AS on Monday: "While I write these lines I feel cold, strange and incredulous."
But he gave a similar prognosis to Sanchez Vicario, saying that Soderling played the match of his life, while Nadal's game deserted him.
Newspapers from Nadal's native Mallorca were forgiving with one of their favorite sons.
Ultima Hora led with "Nadal is human" while Diario de Mallorca had "Nadal's saddest day in Paris" on the front page of their web edition.
In a blog under the story on Diario de Mallorca's Web site, readers were united in their support, calling for Nadal to come home for a well-earned rest among friends.
"Don't worry. For the one you lost you have won many more. You are still No. 1. You deserve a good rest, enjoy Mallorca and its beaches," one blogger wrote.