They were denied victory by Francesco Totti, aged 38 years and three days, equalising for Roma in the first half at the Etihad Stadium to become the oldest scorer in European club football history.
Totti chipped the ball over goalkeeper Joe Hart for his landmark goal after 24 minutes which resulted in City failing to win their first home match in the competition for the fourth successive season -- even after they went ahead with a fourth-minute penalty from Sergio Aguero.
City manager Manuel Pellegrini endured a frustrating night against the in-form Italians, who had won all six matches they had played so far this season in Serie A and the Champions League, and admitted his team now have a tough task to qualify for the last 16.
"We are disappointed to have just one point after playing here at home against a very good team," Pellegrini said.
"It was frustrating because we did not play the way we normally play at the Etihad. We already have a lot of experience in the Champions League,” he added.
"We have played in it for the last three years but today (Tuesday) was not our day. We hope we can improve in the future because we want to qualify for the next round, but it is not going to be easy against some very good teams,” he said.
Despite the experience they have gained since 2011 when they joined Europe's top table, City appear not to have learned the lessons of their previous campaigns.
By losing their opening match 1-0 at Bayern Munich and failing to win on Tuesday they are already five points behind Bayern, who top the group after two wins.
In their three previous campaigns they have drawn at home with Napoli, Borussia Dortmund and lost to Bayern and only once, last season, have they got out of the group stages when they reached the round of 16 and were beaten by Barcelona.
The slow start to those campaigns cost them dearly and this one is showing every sign of going the same way unless their form in Europe improves dramatically.
With two matches played Bayern, who won 1-0 at CSKA Moscow on Tuesday, have six points, Roma have four, City one and CSKA Moscow none.

Despite making a great start, City allowed Roma to dominate much of the first half and only some excellent goalkeeping from Hart kept them in the game, even though they played marginally better after halftime.
City went ahead when their former defender Maicon put his arm around Sergio Aguero and pulled him down, leaving referee Bjorn Kuipers no alternative but to award the penalty.
The Argentine swept home sending Roma's stand-in keeper Lukasz Skorupski the wrong way.
Hart was then the busier keeper as Roma took control for long periods, with Miralem Pjanic and Gervinho forcing the England number one into some vital saves.
One subplot saw Frank Lampard, who came on for the last 33 minutes, face his old Chelsea team mate Ashley Cole, now at Roma, and it was Cole who enjoyed the result more than his former colleague.
Cole, playing his first match back in England since moving to Italy in the close-season, said: "It was a good performance after going down so early in the game, we showed a lot of character, determination and belief and maybe should have won. We can be proud of ourselves today."

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