The Italian believes his side can reach the Champions League knockout phase at the expense of Juventus but has warned of the threat posed by Copenhagen in Denmark
The Danish side have recorded four wins and three draws in the group stages against the likes of Manchester United, Barcelona and most recently Juventus on home soil, but Mancini is confident his outfit can achieve a positive result and maintain their push for the knockout phase.
"Tomorrow's match will be very difficult for us," the Italian told reporters. "Copenhagen have a good coach in [Stale] Solbakken.
"We were in a difficult position following the 6-1 defeat against Real Madrid but now we are alive. This is a tough group but anything is possible.
"It will be a different game from the one in Istanbul because Copenhagen are strong at home.
"I am very happy with my players, who are working hard and improving all the time.
"Juventus and Real Madrid are favourites to progress but I believe we can go through."
Copenhagen will be eliminated from the competition with a defeat, but coach Solbakken expects a much tighter affair than their 3-1 defeat in Istanbul.
"I am certain the game will be a tight affair with few chances for either side. I will be extremely disappointed if there is a significant gulf in class between the two teams as there was in Istanbul.
"Galatasaray’s first-half performance was the best I've seen them play this season. In Istanbul, the first 20 to 25 minutes killed us. We surrendered possession in dangerous areas. That is now in the past, however, and we need to get back to what we do best.
"A few players may be asked to play in different positions tomorrow. The formation is something I will sleep on. Maybe a player will score in my dreams and therefore start, or I’ll have a nightmare and he will be on the bench.
"Losing [Wesley] Sneijder is a big blow for them, but I watched their last match and they did very well after he went off. We need to concentrate on our own game and be disciplined in defence."