Rayo started their campaign with a 3-0 victory over newly-promoted Elche but were brought crashing back to earth at the Vicente Calderon on Sunday and Barral believes that could work in his side's favour when the teams clash on Friday night.
"We can take advantage of the fact Rayo will be feeling down," said Barral, whose side were thrashed 7-0 by Barcelona in their opener before playing out a 0-0 home draw with Sevilla in their next match..
"We'll go there with the aim of taking all three points, which would serve us very well and mean we can go into the international break in a relaxed mood."
Barral, who played up front on his own against Sevilla, could face competition in attack from new signing Baba Diawara, who has been named in the squad for the match with Rayo.
Another piece of good news for the visitors is the return of midfielder Pape Diop and forward Nabil El Zhar from injury.
Rayo, meanwhile, could hand a debut to attacking midfielder Iago Falque, who has joined on loan from Tottenham Hotspur as cover for Jose Carlos, who will not return to action until March.
Mexican forward Nery Castillo is still injured and will not face Levante, but Ruben Martinez, who was Rayo's first-choice goalkeeper last season, is expected to step in for David Cobeno, who played in the opening two matches.