Mancini believes preventable errors cost his team in Madrid, and he feels they must improve quickly to reach the knockout rounds.
The Italian is optimistic, though, that if the Blues manage to up their game and make it beyond the group stage, they can go all the way.
"Like we have improved (over the years) in the Premier League, we need time to improve in the Champions League, but we don't have a lot of time - only five more games," Mancini said.
"We need to not concede easy goals to drop points like we did against Real Madrid. If we want to go through, we need to improve very quickly."