The Brazilian fullback was defiant after the 1-0 loss to Valladolid, though Sergio Busquets accepted that the Catalans simply were not good enough.
Fausto Rossi's goal ensured that Gerardo Martino's men sit one point behind Real Madrid, which has played one game more and has had arguably a tougher fixture list, but the Brazilian fullback was defiant that the Catalans should not be written off just yet.
"We will fight as long as there's a chance of us winning La Liga," Alves told reporters. "Those who cannot trust in us should get off the boat. Our feelings are like those of having lost La Liga in the dressing room. It impacts our chances very negatively, but we will continue to fight.
"Valladolid simply took advantage of their chances and we did not get any luck. There is no time for regret though. We have a very important game on Wednesday, against Manchester City in the Champions League, and we will be eliminated if we fail in that."
Sergio Busquets did not try to defend the performance and thinks that the loss at the Jose Zorrilla will definitely harm Barca's hopes of retaining the Spanish league title.
"We did not have the right attitude," the midfielder said. "We made things very difficult for ourselves. We did not show up in the way we needed to if we wanted to win. The first half was very poor. In the second half we tried but we just could not score. It's a very tough loss. We're now in a difficult situation in La Liga."
Barca will hope to return to winning ways at Camp Nou when Manuel Pellegrini's men visit midweek, with the visitors needing to win by at least two goals to have any chance of reaching the quarterfinals of Europe's elite competition.