City can longer no longer reach the knockout stages of the Champions League after collecting just three points from their first five group games.
Mancini's men made amends for a similar failure last season by going on to win their first league title in 44 years and the focus will now shift mainly to repeating that success.
With expectations continuing to rise at the Etihad Stadium, it was suggested to Mancini that the pressure on him to achieve that will be greater than a year ago, but he disagrees.
The Italian said: "I think we could be disappointed because we wanted to go and play the February stage in the Champions League, because we have good players and these players probably deserved to play in this competition.
"But we don't have pressure. We know we have a chance to win if we stay together in a difficult moment like now, but we do not have pressure because we went out of the Champions League."
For all their vast wealth, power and status as Premier League champions, City remain novices on the Champions League stage.
Although some of the European performances have been lacklustre, Mancini feels it is sometimes forgotten how far the club have come over the last few years.
He said: "We are Manchester City - we are not Real Madrid, Manchester United, Bayern Munich, who are used to winning every year for 100 years and have big histories.
"We are Manchester City and for 35 years we didn't win. Now in two years we won three trophies and I think that is good for us.
"It is clear we want to win every year if possible but this is impossible because in football only one team will win the Premier League and the Champions League. The other teams can't win."
With City still unbeaten in the Premier League - and top of the table prior to this weekend's fixtures - the situation is far from dire for Mancini.
But the team have still largely lacked the dynamism they displayed early last season and they will face a stern test of their credentials at Chelsea this weekend, whatever the recent turmoil at Stamford Bridge.
Mancini said: "I think that we had a problem, we had players injured and we are on the top. I think we can improve more.
"Also, I think this championship will be stronger than last year because I think also Chelsea will fight for the title.
"There are three (teams) in this moment."
City captain Vincent Kompany is doubtful for the match having suffered a knee injury in the Champions League draw with Real Madrid on Wednesday.
The Belgian battled through to the end of the match but left the stadium on crutches and was to undergo a late fitness test.
As the heart of City's defence, his absence would be a major blow for Mancini, who has dismissed concerns over the player's recent form.
Mancini said: "I think Vinny maybe started this season so-so but now, in the last month, he played really well. Vinny is an important player for us."
City will face a Chelsea side hoping to restore stability after a tumultuous week which has seen manager Roberto di Matteo sacked and Rafael Benitez - like Mancini, a former Inter Milan boss - installed as his replacement.
Mancini said of Benitez: "I know him but I don't know him very well.
"As a manager I spoke with him many times before he went to Inter.
"He won trophies in Spain, England - and won a Champions League at Liverpool. I think he is a good manager."