A brace from Aritz Aduriz condemned them to a fourth straight defeat.
But Ayestaran stated: "Both me and the players are capable of turning things around.
“When you concede a goal obviously there'll be defensive errors involved. We're having problems but it's more about specific moments, nothing deeper."
Asked if his job is at risk, the coach added: “I can't think of that. I need to concentrate on getting us out of this situation and boosting the team's morale ahead of the match against Alavés."