The Yellow Submarine finished fourth in the Primera Division last season but have stumbled out of the blocks this year, winning just one of their opening six league games.
Roig told AS: "We have the best coach for this team. Garrido is a great coach and a club man. Last season was spectacular and this year will not be any less so. I have full confidence in its possibilities.
"Things are not as bad as some are suggesting. We are a healthy club who does not owe anything to anybody.
"We have had a bad start to the season but things have been exaggerated."