The Premier League champions looked set to banish the memory of their last-gasp 1-0 defeat at Bayern Munich in the Group E opener as Sergio Aguero converted a fourth-minute penalty.
But City proceeded to be largely outclassed by their technically gifted opponents in the first half, with Francesco Totti's delicate chip - which made the veteran forward the oldest goalscorer in European club football history - the least Roma's efforts deserved.
One point from two matches leaves City five and three points behind Bayern Munich and Roma respectively, meaning victories in back-to-back matches against CSKA Moscow look like a must if they are to avoid a third group-stage exit in four seasons.
"I think that the point, maybe playing at home is never good, but [you] also have to consider that we played against a very strong team in a good moment," Pellegrini told his post-match press conference.
"When the other team scores, it's not just one or two players' problems – he [Totti] had too much space in that play. Maybe the movements were not correct but today we didn't play in the way we normally play to score goals.
"In the last 20 minutes it was more similar to the team we see here every week. We must keep fighting for the next 12 points and then we will see who qualifies for the next round.
"It will depend on how we play the next games whether we qualify. One point from six is tough but we're just three points behind Roma. I hope next time in Russia we can win then we will see what happens in the other game between Bayern and CSKA. Today was not our day."
There was a marked improvement in City's display after both the half-time introduction of James Milner and Frank Lampard's entrance before the hour, as Roma no longer outnumbered their opponents in midfield.
Nevertheless, Pellegrini refused to blame his selection of two strikers in Aguero and Edin Dzeko, claiming City's poor ball retention was more of a problem than his chosen formation.
"We didn't play well in the first half – we started well in the first 25 minutes but then we lost the ball too easily," he said.
"In the way we played last game [Saturday's 4-2 win at Hull City], we played very well with two strikers.
"It was not an easy decision to change from the beginning. We play a lot of games against a lot of strong teams this way and we do very well.
"Maybe today we started losing balls and didn't have enough midfielders to recover it but I don’t think having two strikers on the pitch was the reason we didn’t win.
"The biggest problem was that we missed many easy passes."
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