Real trail their arch rivals by nine points with 14 matches played, and with Barcelona having won all but one of their last 12 games, the former Sevilla coach faces a daunting return to Spanish league action at the Nou Camp on Saturday.
Ramos, a former coach of Barca's B side, moved quickly to shoot down Schuster's claim last weekend that it was impossible to beat the Catalans, insisting that Real have the quality to win in any stadium in the world.
Real's 3-0 Champions League victory over Zenit St Petersburg on Wednesday, his first match in charge, had given the team a confidence boost that would help them on Saturday, he said.
"I was pleased with the attitude of the players tonight," he told reporters.
"Little by little, and as the players gain confidence in the new set up, I think things will improve.
"We have some superb players. They are all internationals and if they play at their best we have a chance to win."
Suspensions for Dutch winger Arjen Robben and left back Marcelo, and a number of injuries including defenders Gabriel Heinze and Pepe, make the task of putting together a competitive side all the harder for the new coach.
Barcelona, by contrast, have close to a full squad available and coach Pep Guardiola rested eight first-choice players for Tuesday's Champions League match against Shakhtar Donetsk, including Lionel Messi and the league's top scorer Samuel Eto'o.
"We are really looking forward to the kickoff and full of confidence that we can win," said midfielder Xavi, who has been in sparkling form this term and was also rested on Tuesday.
Stretching their lead over Real to 12 points would give Barca the luxury of being able to afford to slip up elsewhere, he added.
The Spain international cautioned that it was impossible to write off Real at this stage of the season as they had recovered from a similar situation two years ago and gone on to win the title under Schuster's predecessor, Fabio Capello.
FINDING RHYTHM
In other top of the table action on Sunday, fourth-placed Sevilla, conquerors of Real at the Bernabeu last weekend, host second-placed Villarreal at the Sanchez Pizjuan.
Villarreal are six behind Barcelona on 29 points with Sevilla two back on 27, level with third-placed Valencia. Real are a point behind in fifth.
Although they lost 2-0 to Celtic in their Champions League match in Glasgow on Wednesday, Villarreal have been boosted by the return from injury of striker Nihat Kahveci, their top scorer last season.
"I am feeling very good and already finding my rhythm again," the Turkish international said.
Valencia host struggling Espanyol on Saturday seeking to pick themselves up after last weekend's 4-0 humbling at the hands of Barcelona.
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