Following exits from the Champions League and King's Cup, Real are in danger of ending the campaign with no silverware despite spending close to a quarter of a billion euros in pre-season on players like Cristiano Ronaldo and Kaka.
They trail Barca by six points ahead of Thursday's match at mid-table Almeria and also host third-placed Valencia on Sunday but Pellegrini said his side could still dethrone the Catalans.
"Any advantage at this stage of the season is significant but we still have 21 points to play for," he told reporters. "We have to fight for the league title.
"The thing I am least concerned about is my future and I am not worried about what can happen," added the Chilean.
"We will sit down at the right moment to make assessments. I have one more year on my contract and I hope to complete it and there has been no indication from the club that it won't be completed."
If points are dropped against Almeria or Valencia, Madrid's demanding fans could turn against Pellegrini and president Florentino Perez may decide enough is enough.
The Madrid-based sports media are already speculating about a potential replacement, with Liverpool's Rafa Benitez, Inter Milan's Jose Mourinho and Chelsea's Carlo Ancelotti among the names being mentioned.
Bayern Munich's France playmaker Franck Ribery has also been linked by the media with a move to the Spanish capital.
With midfielder Xavi controlling the match, Depor became the latest Barca opponents to spend long periods chasing the ball and managed only five shots to the home side's 21, according to figures on the club's website.
Pep Guardiola's side made 808 passes to Depor's 275 and if both teams had scored from all their shots on target the result would have been 11-3.
Guardiola said Saturday's match at Espanyol was the key game in the run-in to the end of the season and predicted a "terribly difficult" match.
"We have to prepare very well because they are serious," he said.
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