Real had the chance to close within two points of league leaders and city rivals Atletico Madrid but could only draw 1-1 at third-bottom Real Valladolid on Wednesday, their second consecutive stalemate that was compounded by injuries to attacking duo Cristiano Ronaldo and Angel di Maria.
The result left Carlo Ancelotti's men in third spot, four points from the summit with two games remaining against Celta Vigo and Espanyol.
While Real's destiny is out of their hands, the club will continue to fight as long as they remain a mathematical chance of success, according to international defender Ramos.
"It's practically lost now, but whilst there's still a mathematical chance," said Ramos, who opened the scoring at the Estadio Municipal Jose Zorrilla. "Real Madrid are obliged to keep fighting.
"It's been a long season and the body can feel it now."
Real were on track to secure maximum points until Valladolid substitute Humberto Osorio struck five minutes from time.
The Colombian striker had only been on the field for 12 minutes when he levelled proceedings.
Ramos says his team-mates were punished for their lack of concentration during the closing stages.
"With 10 minutes to go, we've committed the sin of relaxing and against a side who are fighting for survival, who always make things difficult," the 28-year-old said.
"We were neglectful and they caught us out."
Meanwhile, veteran Real midfielder Xabi Alonso says he is 'annoyed' with the team following Wednesday's result that all but ended their title aspirations.
"It would take a few improbable results (to get us back in the title race) but let's wait and see," he said.
"The game was not in control, it was difficult, but I'm annoyed by everything, with the team and with ourselves because we failed to give importance to the final 45 minutes of the match."
