Iñaki Williams put Athletic Club ahead in the 14th minute, finishing after a pass from his brother Nico. Luka Sučić levelled for Real Sociedad in the 30th minute, but Berenguer restored the hosts' advantage from the spot shortly before half-time after Nico Williams went down under a challenge from Jon Mikel Aramburu.
The penalty decision dominated the reaction from the visitors, with Real Sociedad coach Pellegrino Matarazzo convinced that Aramburu had played the ball.
"The match was decided by a penalty where Jon clearly touches the ball. It is very, very disappointing, especially because we have technology that shows that Jon touched the ball, Nico touched it first and the chip registered that Jon touched it second," he said.
"For me, it is clearly not a penalty and I don't understand why VAR didn't intervene and overturn it, because that is the decisive goal in this match. I don't think this game deserved that mistake to be the decisive goal."
Matarazzo was particularly frustrated by what he perceived as the speed with which the decision was accepted.
"What bothered me more? I felt they didn't even check it. I felt they were certain within about five seconds that it was a penalty. That is what I don't understand, because we clearly see on the bench that the ball changes direction. That is what bothers me most: such a decisive decision was not checked twice."
Athletic coach Edin Terzić preferred not to become involved in the debate, pointing to previous decisions that he felt had gone against his side.
"There have been difficult decisions against us on other occasions and I never said anything about them. I won't do so now either, because I don't like talking about referees, either positively or negatively," he said.
Terzić was delighted with the performance, particularly the intensity his players showed during the opening half-hour.
"We are very happy with the victory. The message is that we are on the right path. The first 30 minutes were incredible in the way we pressed and created opportunities. The job is to extend those 30 minutes and make that level of performance last for the full 90."
He also singled out goalkeeper Unai Simón, whose saves helped Athletic protect their lead as Real Sociedad pushed for an equaliser.
"Unai has shown why he is the best goalkeeper in the world. Real Sociedad scored with their first opportunity and then Unai saved us and gave us stability. But many players performed very well to make this victory possible."
The result was particularly valuable for Athletic, who needed points against a Real Sociedad side arriving after four consecutive victories.
"We have to climb the table because we need points, and Real Sociedad are a very difficult opponent," Terzić added.