The Brazilian full-back was defiant despite losing 1-0 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 having played a game more but the Brazilian full-back was defiant that the Catalans should not be written off.
"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 concedes Barcelona's mentality was not correct and believes the loss at the Jose Zorrilla will definitely harm the club's hopes of retaining their 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."