The LaLiga champions snatched a point through Lionel Messi after Willian Jose opened the scoring but were second-best throughout the encounter at Anoeta.
Sociedad twice hit the woodwork through Carlos Vela and saw a Juanmi goal unjustly ruled out for offside, while Barca mustered only two shots on target during one of their worst displays of the season.
And Luis Enrique was left aghast at the standard of his players, admitting that they fully deserved to lose the match.
"If I look at the result, it's the most positive assessment I can give from this season," he told Barca TV. "To finish 1-1 is almost a miracle. Winning would have been unfair and I have to congratulate Real.
"We couldn't even string five passes together. Without the ball, we were disastrous."
He continued in his media conference: "They pressed us with six players and we didn't find the middle-range and long-range passes.
"We didn't even win five per cent of the duels. If you don't match up in this type of duel and you concede the advantage, there's little you can do.
"In the second half we improved a little but nowhere near enough. We drew the game because of an isolated bit of play between Messi and Neymar, but little else.
"We don't deserve to take a point back to Barcelona."
Gerard Pique told Movistar Plus that Barca could not hope to defend the title if they repeat such a display, but Luis Enrique felt the defender's comments simply came in the heat of the moment.
"I understand that interviews at the end of a game are dangerous. You haven't adjusted to the reality of the situation," he said.
"To give up on LaLiga on matchday 13 would seem an exaggeration to me."
Barca head into next weekend's Clasico with a six-point deficit to leaders Real Madrid, and Luis Enrique has promised fans that they will produce a better performance.
"We have to start improving. We've produced the worst game of our era and we'll certainly see a different Barca in the Clasico," he added.
"The battles will be important and they will be decisive. I'm sure that we will fight."