Nainggolan and his teammates were unable to break down a resolute Atletico defence while also denying their seasoned European opponents the chance to score.
The result left Roma and their opponents on one point, as Chelsea lead Group C following their 6-0 thrashing of Qarabag.
After the match, Nainggolan praised his side while also acknowledging the impressive work of goalkeeper Alisson Becker.
He said: “It’s an important point for the confidence. We managed to create some good chances in the first half – their goalkeeper made a good save from my shot. Then Alisson after that made quite a few. We feel a draw is a good result against what is a top side.”
He added: “We are at the start of the season, there are new tactics and a different style of working to what we were used to.
“It’s normal that it will take a bit of time to be 100% for 90 minutes. But only through work will we get better at this.
“We have changed a lot – to a new style of play with a new coach. It will take time to do everything perfectly. We are not robots, we are working on it and we hope to keep getting better in a number of ways.”