The European and Spanish champions, who have won three consecutive league crowns, are in the unfamiliar position of trailing their arch-rivals with two weeks to go until the first league 'clasico' of the campaign at the Bernabeu.
The Madrid-based sports press made much of Real's advantage with Marca and AS both trumpeting the new six-point gap on their Sunday front pages.
"Many people would hand out the league trophy now and are setting off rockets," Barca's Brazilian defender Dani Alves told a news conference on Sunday.
"They don't hand out the cup now. Luckily for us there is still a long way to go and one of the keys to this team is that they never give up."
Real swept aside city rivals Atletico Madrid 4-1 on Saturday for their 13th consecutive victory in all competitions, and Jose Mourinho's team opened up a gap which could prove difficult to bridge, especially if they were to be victorious on December 10.
Real and Barca, the world's two richest clubs by income, have dominated La Liga the last couple of seasons with both sides racking up over 90 points, leaving third-placed Valencia more than 20 points behind in third.
With draws being called 'the new defeats' by local media, Real, who have only lost once at surprise early pacesetters Levante earlier in the campaign, would appear to hold a psychological edge in the run up to the first 'clasico'.
"There is still a long way to go," Guardiola said on Saturday. "We all know we are competing against a great rival and have less room for more slip ups, but we will lift ourselves and move forward again."
Barca's 27-game unbeaten run in competitive matches stretched over six months, and they last suffered a defeat in April last season, when they fell 2-1 at Real Sociedad in La Liga.
They have a midweek league clash at home to promoted Rayo Vallecano on Tuesday, a game rearranged because of their participation in next month's Club World Cup, and then host Levante next weekend, before returning to face their title rivals.
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