The Spain international defender has called on his team-mates to avoid letting any complacency set in, and turned his attention to the upcoming Clasico
Los Blancos sit seventh in the Spanish top flight, on seven points, while the Blaugrana sit first, eight points ahead of their rivals with a 100 per cent record.
And Alba believes the early points difference could be crucial this campaign, although the summer signing insists Atletico Madrid and Malaga could be contenders this season too.
“We are eight points [ahead] and it's very important,” the 23-year-old told AS. “Now we have to think about getting the three points against Sevilla.
“Hopefully we can keep the difference [between the clubs] up to the Clasico. But I would not rule out Atletico and Malaga [winning the league].
“We'll see if we can beat Madrid, it would be great to extend the distance. It was unthinkable that Madrid lost these games, so we are warned: it can happen to us.”
Barcelona play Sevilla away on Saturday, with kick-off at 22:00CET.