Barcelona went behind in the encounter and De Jong admitted that the visitors found it tough to deal with their opponents to begin with.
"It was an intense game, with lots of pressing, and we weren't very comfortable, but we were able to react and come back," De Jong said.
De Jong also complained after Barcelona weren't given a penalty at the end of the game.
Gerard Pique appealed for a spot-kick after he went down under the challenges of Diego Llorente and Mikel Merino.
His claims were waved away by referee Gil Manzano, who had previously awarded a penalty against Barcelona after Sergio Busquets grabbed hold of Llorente in the first half.
"If you give the first penalty for Real Sociedad, you have to give the one on Pique," De Jong said after the match.