As in the midweek defeat to Trabzonspor, Inter coach Gian Piero Gasperini heard boos echoing around the stadium and was left still waiting for his first win in charge after four attempts.
Roma boss Luis Enrique, on the other hand, will know that what would normally be regarded as a good point in Milan does little to help his own cause.
There was also a worrying injury for Roma goalkeeper Maarten Stekelenburg, who was taken to hospital after receiving a boot to the head from Inter defender Lucio and was reported to have briefly lost consciousness.
As for the result, after such a tense encounter with few clearcut chances, neither coach can have too many complaints that their first win of the season will have to wait until at least the middle of next week.
Luis Enrique sprang a few surprises in his team selection, choosing midfielders Simone Perrotta and Rodrigo Taddei as full-backs and leaving Bojan Krkic out in favour of Fabio Borini, making his first start of the season.
And he was forced into another change after just 15 minutes when Stekelenburg had to be carried off the field and taken to hospital after his collision with Lucio.
His replacement Bogdan Lobont was promptly tested by Wesley Sneijder, whose shot from 20 yards skidded off the surface, but was saved at the second attempt by the Romanian.
That was Inter's first shot of the game and Roma's first arrived moments later from Borini, whose effort was too close to Julio Cesar to cause any danger.
Inter went closer when Yuto Nagatomo's shot curled over the bar from the edge of the area in the 36th minute.
Roma followed Inter's lead in creating, then spurning, another chance in the first minute of the second half with Osvaldo the man to be denied by Julio Cesar.
The best chance of the game fell to Sneijder in the 85th minute, but his shot was deflected wide by Simon Kjaer.