"We need to improve and ensure that our games are more consistent, because right now they really aren't," Diego Simeone said.
"It's always tough when the opposition closes up shop. We didn't have the kind of speed or skill needed to undo them.
"The most important thing for us is to improve and grow and I'm confident we're heading in the right direction with the work we're doing."
Atleti huffed and puffed as they attempted to find a way back into the match, but were kept out by admirable defending from the hosts.
Tomas Pina missed a glorious chance to double Alaves' lead nine minutes from time, but fired over when unmarked on the penalty spot -- but his side hung on to claim a first victory over Atleti since 2003.
Alaves moved off the foot of the table.