Real Sociedad took the lead through Orri Óskarsson in the 28th minute of Thursday's Europa League meeting, but Corentin Tolisso equalised shortly after half-time to earn Lyon a point.
Matarazzo felt his team had controlled much of the second half and created opportunities to secure victory, but acknowledged that their attacking play lacked the quality required to break down the visitors consistently.
"I agree that we played a very good match, especially in the second half. There was a lot of control and many situations in which we could have created more chances," he said.
"It wasn't our best attacking performance today. If you want to break down a good, very good Lyon defensive line or block, you need a little more quality on the pitch. But overall, I think the players competed very well for 90 minutes."
The Real Sociedad manager was also disappointed with the manner in which his side conceded, believing the equaliser came too easily.
"We conceded the goal too easily, and also the opportunity that came towards the end of the match. Apart from those situations, they didn't create many chances against us, so there are a lot of positives we can take from this game."
Matarazzo identified precision, speed and decision-making as the areas where his team had fallen short.
He pointed to two opportunities involving Gonçalo Guedes, both of which could have produced a more dangerous situation had the final pass been better.
"Yes, it was a question of precision, speed and decision-making. I remember two very clear situations with Gonçalo in the second half. In one, the goalkeeper was out of position; in the other, there was a huge space between the centre-backs, which we had analysed before the match, but the pass was too slow and imprecise, allowing the goalkeeper to intercept it.
"There were also transitions where we didn't identify the central channel that was unprotected. There were two or three specific decisions where we need to be more precise to turn our dominance into clear chances."
The draw was another setback for Real Sociedad's hopes of finishing in the league phase's top eight, although Matarazzo does not want to look too far ahead.
He considered a point a fair reflection of the contest, while feeling his side could have taken more from it.
"It's difficult to separate the matches because there are so many games. I think a draw is a fair result, but there was more in this match than we managed to get out of it."
With four fixtures remaining, the manager knows his team need to start collecting victories.
"We want to achieve our objectives and, as I said before, we need three points in every match."