The Premier League champions failed to progress beyond the group stage of the competition in 2011-12, but the Italian says that his players have learned from last campaign's mistakes.
"The Champions League is a different competition but the football is the same and it's still 11 versus 11," he said. "The problem is you're always playing against other countries' best teams, which means it's always difficult.
"I hope I can improve my record in the Champions League and I think we are capable of winning it, but we're in a tough group again. We've got five games left and we can progress."
However, Mancini admits that it will not be easy for City to win Europe's premier club competition and that they need to tighten their defence.
"High expectations are normal in football, but I know just how hard it is to win the Champions League," said the 47-year-old. "It's only our second year and the second time we've got the toughest group in the competition.
"Just as we've improved in the Premier League, we'll need time to improve in the Champions League, but we've not got time as we've only five games.
"We need to stop giving away easy goals like against Real Madrid and improve quickly."