Sevilla slipped to a 2-0 defeat at promoted Las Palmas on Wednesday and have just two points after managing two goals and conceding eight in five outings in Spain's top flight this term.
Vitolo, a Spain international, said the players were hoping victory against Rayo would kickstart their domestic season with a home game against champions Barcelona looming the following weekend.
"These are difficult moments and as a footballer you are affected because you work day to day and the victories don't come," he told the club's radio station on Thursday.
"The season has just started but we have to wake up, get ourselves together and finally win a match."
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Sevilla qualified for the Champions League group stage by winning a second consecutive Europa League crown last season and made a strong start in Group D by beating Borussia Moenchengladbach 3-0 this month.
After hosting Rayo on Saturday, Unai Emery's side visit 2014-15 beaten finalists Juventus on Wednesday before European champions Barca visit in La Liga the following Saturday.
Vitolo said he understood the fans were upset but urged them to get behind the team at their Sanchez Pizjuan stadium in the Andalusian capital.
"In these situations criticism doesn't help the team because we are very upset," he said. "The dressing room is feeling bad and we have to find a solution to this together.
"When the first win comes everything will change but we have to get it done. The team raised a lot of expectations before the season started and it's natural no Sevilla fan is happy the team has two points from five games.
"I cannot say anything more than we will try to turn the situation around and if we are united, team and supporters, we can make progress," added Vitolo.
(Reporting by Iain Rogers, editing by Tony Jimenez)
