City can 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.
"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," the Italian said. "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."
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 will undergo a late fitness test.