Real Sociedad built a three-goal lead through Jon Martín, Arsen Zakharyan and Gonçalo Guedes before Deportivo responded through Mario Soriano and Yeremay Hernández's penalty. The hosts then had to withstand sustained pressure after Pablo Marín was sent off, with Deportivo also losing Lorenzo Amatucci to a late dismissal.
Matarazzo admitted his side had not produced their best football, but was pleased they found a way to secure three important points.
“Without playing a good match and without showing our best football, we managed to go 3-0 ahead and had some very clear chances,” he said.
“Then, after the 3-2, the team showed a very good reaction and we had a great chance to score the fourth. They had some opportunities, but we also played a good match and won. We suffered, but we took the three points, and for me that is another step forward.”
The Real Sociedad manager accepted that his team should have controlled possession better after establishing their advantage.
“At that moment, we should have had more possession and more control of the game. I think we played too much towards our transitions, lost the ball and had to defend again,” he said.
“It would have been intelligent for us to keep the ball more and move it faster. We also need to move more ourselves.”
Matarazzo was reluctant to criticise the referee over Marín's dismissal, which came during the penalty incident that allowed Yeremay to make it 3-2.
“I didn't see Pablo's red card on television. It is the referee's interpretation, and I think we have to accept it,” he said.
“If Pablo commits a foul in that situation, it is a red card because it is a clear goalscoring opportunity. I don't know whether it needed to be a foul and a red card, but that is what happened. We accept it and move forward.”
Hidalgo, meanwhile, felt Deportivo had grounds to be awarded the penalty after Luismi was challenged in the area.
“For me, today that is a penalty on Luismi. He touches him low down and with his arm, and it unbalances him. At the end of the match the referee explained it to me. I accept the explanation, but I don't agree,” he said.
The Deportivo coach also believed his team had not been decisive enough in key moments.
“We have to be smarter and more decisive in certain phases of the match, especially in our own area,” Hidalgo said.
Despite the defeat, he took encouragement from the character his players showed in fighting back from three goals down.
“It gives me strength. I am angry that we didn't equalise, but this team has soul, and that makes me happy.”
Matarazzo also praised Deportivo's organisation, describing them as a well-coached team with quality players who understood how to operate in every phase of the game.