Madrid looked near certainties for the title when they embarked upon a strong run at the turn of the year, but back-to-back defeats to Barcelona and Sevilla mean Los Blancos are now three points behind leaders Atletico Madrid, who lead second-placed Barca by one point.
Only six games remain, but Alonso is refusing to give up on the title just yet.
"In the league we have lost the advantage that we had, but we need to keep fighting because there could be surprises," Alonso told his club's official website.
"The teams that beat us were in great form, we didn't play well in two games and we committed errors that we paid very heavily for."
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