Roma topped the group while Atletico finished third and drop into the Europa League in the new year.
Davide Zappacosta had the first shot of the match but his effort sailed over the bar while Alvaro Morata’s strike curled just wide of Jan Oblak’s goal.
Morata had another shot saved by the Atletico Madrid goalkeeper after Victor Moses had cut the ball back to him before the Blues striker fired wide from a tight angle.
Just past the half-hour Zappacosta’s right-footed effort was turned away by Oblak for a corner as Chelsea continued to press for the opening goal.
Atletico started the second period well and Thibaut Courtois saved Antoine Griezmann’s free-kick before Eden Hazard’s shot was blocked by Stefan Savic.
Chelsea then enjoyed a purple patch with Andreas Christensen heading straight at Oblak before Hazard’s shot was deflected over the bar and Morata’s header was kept out by the Atletico goalkeeper.
The Spanish side hit the post when Filipe Luis’ dipping shot beat Courtois but they took the lead in the 56th minute with a back-post header by Saul Niguez after former Chelsea striker Fernando Torres had won the flick-on at a corner
Christensen missed with another header and Pedro was denied by Oblak before Chelsea equalised with 15 minutes left when Cesc Fabregas’ cross was turned towards goal by Hazard and Savic put the ball into his own net.
Morata and substitute Willian wasted outstanding chances to win the game for Antonio Conte’s side but Chelsea had to settle for a draw.