City were beaten by a last-minute strike from former player Jerome Boateng on matchday one, with the defender's goal enough to give Bayern Munich a 1-0 win at the Allianz Arena.
Roma travel to the Etihad Stadium this week on the back of a comprehensive 5-1 win over CSKA Moscow and have won all five of their Serie A matches this season, conceding only one goal.
Hart, who is set to regain his starting place in goal after being left out of Saturday's Premier League victory at Hull City, is aware of the danger Roma pose, but claims City are fired up to get their Champions League campaign up and running.
"It's obviously a big game for us," said the England international, who was outstanding in City's loss at Bayern. "It was disappointing to start with the loss out in Munich but it's the Champions League and luckily it's not knockout straight away.
"We need to start our home Champions League campaign with a win but we know Roma will be tough.
"We're more than up for this. We know how well Roma have been playing but we are ready."
Meanwhile, City manager Manuel Pellegrini revealed forward Stevan Jovetic will be available for the clash, but midfielder Fernando will miss out.
"We continue injured with Fernando," said the Chilean. "Stevan Jovetic is in the squad list - he is ready for tomorrow.
"Samir Nasri had surgery yesterday, he will be out for around one month. All the other players are fit."
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