Diego Simeone’s Spanish side had the majority of the chances – including one first-half effort that was cleared off the line by a defender – but were largely inaccurate in front of the goal.
Atletico and Roma dropped behind Chelsea in Group C after the Antonio Conte’s men routed Azerbaijani side Qarabag 6-0 in the other group match.
Atletico has finished runner-up twice in the last four editions of the tournament and was a semi-finalist last season. All four campaigns have ended in defeat to city rival Real Madrid.
They have won their group in each of those seasons.
Roma returned to the competition after year-long absence yet the Stadio Olimpico was far from full for the club’s first European match since the retirement of longtime captain Francesco Totti.
Atletico standouts Antoine Griezmann and Saul Niguez each wasted excellent chances early on.
The visitors were preparing to celebrate when Koke looked set to finish off a counterattack but Roma’s reliable center back Konstantinos Manolas cleared the danger off the goal line.
Approaching the hour-mark, Luciano Vietto was set up nicely with only Roma goalkeeper Alisson to beat but his chip shot was tipped over the bar by the Brazil international.
Niguez was then set up perfectly in the center of the area but aimed his shot directly at Alisson – who had a terrific performance – and missed again from close-range in the 90th.
Roma’s best chance came from Radja Nainggolan with a low, powerful effort following a corner that was stopped by goalkeeper Jan Oblak near the post.
Meanwhile, Simeone and Roma counterpart Eusebio Di Francesco gesticulated on the touchlines with the same energy they used to display against each other in the Rome derby in the Olimpico as players – Simeone for Lazio and Di Francesco for Roma.