Depor's La Liga campaign has been woeful so far, with just two wins from 15 attempts leaving them at the foot of the standings.
However, victory on Monday would not only lift them off the bottom but out of the relegation zone, although Oltra says they need the Riazor crowd to get behind the players.
"The fans are the only ones who have not failed so far," he said.
"If they have to show frustration or anger with someone then show it to the coach, not to the players as they need full confidence.
"If they have to show anger, show it at the end if the result is not satisfactory, but during the game we need everyone's support."
Oltra at least has some positive team news ahead of Monday's match, with Ze Castro and Carlos Marchena back from injury and Aythami Artiles available following suspension.
Mid-table Valladolid will be looking to pick themselves up from last weekend's 3-2 defeat to Real Madrid, in which they twice let slip the lead.
Coach Miroslav Djukic is a familiar figure at the Riazor, having spent six seasons at Depor as a player, although he will not let sentiment get in the way.
"This is an important match for us," said the Serbian.
"I can not let the team go there without at least trying, that would be my fault.
"We played well against Real Madrid and can be a team of ups and downs.
"We need to send out a message at Riazor, be ourselves and get the win."
Valladolid have injury worries over Patrick Ebert and Jesus Rueda, but Manucho is back in training after an illness.