On coach Alvaro Arbeloa's debut, Real Madrid lost 3-2, with Gonzalo Garcia's injury-time equaliser still being bettered by a second from Jefte Betancor on 94 minutes.
Carvajal later said: "Today we hit rock bottom. We've been knocked out by a Segunda División team and congratulations to them. From tomorrow, we have to be self-critical individually and collectively.
"We still have time to turn the season around. We have two fantastic competitions to fight for. The team isn't at its best right now and we have to work hard.
"We all have to give a lot more and that is the reality. That's the message: we have to go all out. We also apologise to the fans and we are not, myself first, at the level and expectations of this club. We promise to give our all in the games over the next few months so that the situation can be reversed."