Ramos suffered a losing start in the league on Saturday when the champions went down 2-0 to leaders Barcelona at the Nou Camp, and Real are in sixth place after 15 matches, 12 points off the blistering pace set by the Catalans.
The list of Real injured includes defenders Pepe and Gabriel Heinze and midfielder Wesley Sneijder, while knee injuries have ended the seasons of Ruud van Nistelrooy and Mahamadou Diarra.
Midfielder Ruben de la Red might not play again this term after his collapse in a King's Cup match in October.
"We are past our low point and after Christmas we will have players back and two or three new signings," Ramos, who was picked to replace Bernd Schuster on Tuesday, said in an interview with Monday's AS newspaper.
Real would be "a team reinforced and very motivated" and if Barcelona slipped up they would be ready to take advantage, the former Sevilla and Tottenham Hotspur boss said.
"The one sure thing is that (Barcelona) will hit a bad patch at some point, as happens to every team with such a challenging calendar," he added.
In a separate interview with Marca newspaper, Ramos said if the players continued to work with the same attitude they showed on Saturday, they were capable of clawing back the 12-point gap to Barca.
"My primary objective is to get the injured players back," he said. "We will be a different team when they have recovered and I think we have a squad capable of challenging for the league and the Champions League."
Asked what positions the club needed to fill in January, Ramos said: "Clearly a wing back and a central midfielder."
"The club is working on it and I hope they will arrive soon," he told AS. "I want two players with quality and fighting spirit who get stuck in."
