The Brazilian defender is refusing to throw in the towel and stressed that he will only admit defeat when his side are mathematically out of the race for the league crown
The Catalan giants have closed the gap on Real Madrid to seven points following Saturday's 2-0 victory at Sevilla, but Los Blancos have the chance to increase the distance as they host Malaga on Sunday.
After Barca's weekend victory, coach Pep Guardiola stated that the chances of a Madrid slip-up were very slim and, as such, he thought that retaining their Liga crown was no longer possible.
"That is his opinion and everyone is entitled to that, but we will continue to compete," Alves told reporters at a press conference.
"There is always a meaning to everything that the coach says. Ask him about what he said. We will keep fighting.
"The gap is considerable, but tough matches are coming up for Madrid and for ourselves, and we will make an assessment only in the end."
Despite the fact that Barca have already dropped seven points since the start of the year, Daniel Alves rejected the notion that his side's level has decreased.
"We represent the best team in the world and we have to honour this shirt in every match," he added.
The Brazilian defender then stressed that he is not thinking about a potential Champions League final against Real Madrid after the two clubs were drawn in different sides of the bracket.
"It does not matter to me who we can face in the final," he noted. "We have to see off AC Milan without thinking beyond that
"We must be very focused and alert to prepare the tie because Milan are a very tough opponent."