City's hopes of progression to the knockout stages are hanging by a thread after claiming just two points from their first four matches.
Pellegrini's men suffered a morale-sapping 2-1 home defeat to CSKA Moscow in Europe's premier club competition earlier this month in a match that saw them finish with nine men.
The Premier League champions have enjoyed plenty of success domestically in recent years, with two league titles and glory in the FA Cup and League Cup appeasing the club's super-rich owners - at least for now.
However, City's backers still long for European joy - something that has not been forthcoming.
Knocked out in the group stages in 2011-12 and 2012-13, City reached the round of 16 before being eliminated by Barcelona last term.
Ahead of the visit of the German champions in Tuesday's Group E clash, Pellegrini said: "My own pressure to continue to the next round is an important pressure - more maybe than the owners.
"Of course, I think we must be in the next stage.
"A lot of times you don't reach the target you are supposed to do…but we have to play two more games and we will see what happens."
City midfielder James Milner is staying positive and added: "It's two games - win them both and we're through. We can do that.
"We went to Bayern last year and beat them in their own backyard and it's important that we get the three points."
Milner was outstanding in City's 3-2 win at the Allianz Arena last term and scored the winner.
He is likely to be relied on again - as are Frank Lampard and Fernando - given the absence of suspended pair Yaya Toure and Fernandinho, and the injured David Silva (knee).
Edin Dzeko (calf) is also set to miss for City, but captain Vincent Kompany did return from a similar issue in the club's 2-1 Premier League win over Swansea City on Saturday.
Stevan Jovetic and Toure scored in that come-from-behind win that kept the champions eight points behind leaders Chelsea.
Bayern - who lead the group by eight points and have already qualified for the last 16 - had things far easier on Saturday, easing past Hoffenheim 4-0 to extend their lead atop Bundesliga to seven points.
Mario Gotze's stunner set up Bayern's big win as Robert Lewandowski, Arjen Robben and Sebastian Rode also got on the scoresheet.
Bayern last lost a competitive game in April in the second leg of last season's Champions League semi-final against Real Madrid.
And while they have already qualified, Pep Guardiola is sure to put out a team more than capable of causing problems for City, despite a lengthy injury list that contains the likes of Philipp Lahm (ankle), David Alaba, Thiago Alcantara and Javi Martinez (all knee).
In better news for Bayern, Germany captain Bastian Schweinsteiger returned from a long-term knee problem of his own on Saturday.
Bayern beat City 1-0 in September thanks to a superb stoppage-time strike from Jerome Boateng, who they signed from the English club.
The German side have won three of the five competitive encounters between the two but City fans will be hoping history repeats this year.
In both the 2011-12 and 2013-14 Champions League campaigns - in which they played each other in the group stages - Bayern won the first clash before City responded with a win of their own.
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