After their draw with Getafe last weekend, Barca looked like they were out of the title race, but defeat for Atletico Madrid and a draw for Real Madrid left the door open for Gerardo Martino's men - now three points off the lead.
The results mean the Catalan giants could retain their Liga crown if they win both of their remaining fixtures, including the final day clash with title rivals Atletico.
And Alves remains confident Barca will not let the chance of consecutive titles slip from their grasp.
"If we don't win the league then the season is a disaster," he is quoted as telling RAC1. "A lot of opportunities have been given to us and we haven't taken them.
"I have 100 per cent trust in this team and I guarantee you we will not fail."
Barcelona next face Elche in the league on Sunday.
