The champions never looked in danger from the moment Mikel Gonzalez headed into his own net after just two minutes.
Antoine Griezmann then doubled the hosts’ advantage against his former club shortly afterwards to end the game as a contest inside the first 10 minutes.
Sevilla moved level with Valencia in fourth, just four points adrift of Atletico, with a 2-1 win at Levante thanks to first-half goals from Kevin Gameiro and Jose Antonio Reyes.
Barcelona can regain their nine-point lead over Atletico when they and closest challengers Real Madrid are in action against Almeria and Rayo Vallecano respectively on Wednesday.
“Both the goals are down to mistakes we made,” lamented Moyes.
“I don’t think it is a free-kick on the first goal, but we have to defend it and we didn’t. We made mistakes and we made mistakes for the second goal as well.”
Defeat all but ends Sociedad’s outside hopes of qualifying for the Europa League, but the former Manchester United boss insisted he never thought that was a realistic target having taken over the Basque outfit with the remit of avoiding relegation.
“I’ve aways felt like it would be too difficult to make Europe. The distance to make up was too far,” Moyes added.
“We’ve been on a very good run. We’ve had two difficult away games and I think the players have done a lot of good things.”
Sociedad beat Atletico 2-1 when the sides met back in November and came into the game having lost just one of their last eight La Liga games, but were on the back foot straight away as Arda Turan volleyed against the post inside 60 seconds.
The visitors managed to scramble the rebound behind but from the resulting corner, Gonzalez could only flick Koke’s in-swinging delivery into the far corner.
Eight minutes later it was 2-0 as Geronimo Rulli could only parry Koke’s fierce drive into the path of Griezmann, who slammed the ball high into the net but refused to celebrate out of respect to the club he spent nine years with prior to his big money move to Atletico last summer.
“They gave me a lot and I am here thanks to them,” said Griezmann.
“We are playing well and now have the consistency that we need to continue with. It is normal that in the course of a season you have a dip but we are now fighting for the Champions League places.”
Griezmann came close to inflicting more pain on his former employers as he was denied by a last-ditch tackle from Gonzalez before nodding just wide from another dangerous corner.
Sociedad gradually grew into the game, but only seriously threatened Jan Oblak’s goal when Chory Castro’s powerful shot forced the Slovenian into a smart save.
Atletico took the sting out of the game in the second-half with next week’s Champions League quarter-final against Real Madrid in mind.
However, they were still characteristically solid at the back to secure a fifth consecutive clean sheet.
At the other end of the table minnows Eibar ended an 11-game winless run to ease their relegation fears with a 1-0 victory over Malaga.