The Italian manager believes if they can succeed this season it will have a snowball effect. Mancini is fully aware of the history of the club and the fact they last won a major trophy on February 28, 1976 when Newcastle were defeated 2-1 in the League Cup final.
He said: "We have a big chance of winning something. The next 20 days are very important because we play on Wednesday against Aston Villa then the following week in the Europa League."
He added: "We have two options. If we win one trophy it will lead to more trophies. This is important for our team.
"When I accepted this job I knew it was difficult but it is a big challenge and I believe we can win a trophy."
City go into the the Villa game following a lacklustre 1-1 home draw with Fulham on Sunday. Mancini believes his players are feeling the effects of a tough fixture schedule at home and abroad.
However, he would not have it any other way.
He said: "It is better we have all these games because it means we are still involved in every competition. Everything is important for us.
"But our problem is having players injured. When you play every three days you cannot work, only recover with perhaps a light session.
"Is it difficult motivating the players? We are tired here (in our heads) because when you play every three days and use the same players it is very difficult. This is a big problem but only this."