After drawing their curtain-raiser at home to Napoli 1-1, City suffered a 2-0 defeat at the hands of Bayern Munich in Germany last time out.
City now sit third in the pool and five points adrift of Bayern, who also won their opener against Villarreal.
But Mancini is adamant they can force their way back into contention when their campaign resumes next week.
"I am still convinced that we will qualify," Mancini told Il Domani dello Sport. "We've only played two games and four remain.
"I think nine points would be enough to qualify."
He added: "Villarreal have lost their way, they're almost out. Napoli are a strong, well-organised team.
"Bayern Munich are like a steamroller at the moment, crushing everyone. But in Germany, when the score was 0-0, we had two penalty claims turned down."
Mancini's side take on Villarreal at the Ethiad Stadium next Tuesday, while Napoli and Bayern go head-to-head in Italy.
The City boss is hoping for a draw from the encounter in Naples, adding: "It will be very important and for us a draw would be best.
"It would be nice for us and Napoli to go forward in the Champions League together."
Mancini has backed temperamental striker Mario Balotelli to play a key role in City's European campaign, despite his uneven start to life in Manchester since arriving last summer.
"He's going strong and I am convinced that this time it will last," added the manager. "He will be our weapon in the Champions League."
Asked about City's start in the Premier League, Mancini added: "Well, we are first in the Premier League with United.
"We are a real team, we lack only experience. I'm happy."
City have been linked with moves for Napoli forwards Ezequiel Lavezzi and Marek Hamsik but Mancini admits he would have no place for them in his star-studded attack.
"(Lavezzi) is a great player and devastating in his every move. But I would not know where to put him at City," added the former Inter Milan boss.
"The same goes for Hamsik, who I first admired while in Italy. I wanted to take him to Inter when he played for Brescia."