The victory over Getafe last weekend provided welcome relief after a difficult week for the Yellow Submarine, but Roig stressed that the result was not a decisive test of the manager's position.
Villarreal had suffered a heavy defeat against Espanyol before being thrashed by Paris Saint-Germain in the Champions League. The response against Getafe was therefore important for morale, although Roig made clear that the club's faith in Pérez had never depended on a single match.
"Everyone is encouraged and enthusiastic, and that is why we have spent 27 years in the top flight and 18 in Europe. We have backed a very good project and I hope and trust that the results will be good," he said.
Roig also rejected the suggestion that the Getafe fixture had been a personal examination for the manager. Instead, he believes the entire squad needed to respond after a difficult period.
"It wasn't a test for Iñigo, but for the whole team. We will get to a good place, and those who are booing now will applaud later and say they have never booed in their lives. It is during difficult moments, and this is one, that you have to show your support."
The president acknowledged the frustration among supporters but called for patience as the team attempts to find consistency. He believes the club's established record and long-term approach provide grounds for confidence rather than panic.
The Getafe victory also coincided with a significant milestone, as Villarreal reached 1,000 appearances in Spain's top division. Roig described the achievement as a source of considerable satisfaction, made even more meaningful by securing three points on the occasion.
"One thousand matches is a lot. It is a great satisfaction, especially to celebrate it with such an important victory. After the week we have had, it was a reason to be very happy. We have to encourage the whole team," he said.
Villarreal have now collected 15 points, which Roig considers an important step towards the club's immediate objective.
"We already have 15 points, which brings us closer to the first objective, which is to secure our place in the division. Then everything else will come," he added.
Attention will also turn to the Champions League after the international break, with matches against Slavia Prague and Sabah potentially crucial to Villarreal's hopes of progressing.
"In the Champions League we have to get as many points as possible. At the moment we already have three times as many points as last season, but now we have to collect everything we can," Roig said.
For the president, the message remains one of unity and confidence. Villarreal have endured a difficult spell, but Roig is convinced that the project under Pérez deserves time and support.