Neither side could break the deadlock at the Vicente Calderon, leaving the tie on edge ahead of the second leg at Stamford Bridge next week.
"This wasn't our objective. We wanted more but we couldn't find the goal," Diego, who is on loan at Atletico from Wolfsburg, told reporters.
"It's not a bad result. The game is still open and it might be different next time. We have to be smart and take advantage of our opportunities."
Atletico are still unbeaten in this season's Champions League.