Pellegrini???s side must either win or record a score draw against Roma in the Italian capital and hope CSKA Moscow’s result against Bayern Munich goes their way as well.
City, who will be without top-scorer Sergio Aguero at the Stadio Olimpico, have made no secret of their ambition to make their mark in the Champions League this season.
A third exit at the group stage in four seasons could therefore raise questions about Pellegrini’s future but the 61-year-old does not feel his job is under threat.
He said: “I don’t think so. Tomorrow is a very important game and all of us want to qualify but I don’t think that what happens will have some link about the future in my club.
“I have never received any kind of pressure from the club. I hope we are going to qualify but I have nothing to be (concerned) about my future here.”
Roma know that they will go through with a victory but anything less would open the door for City or CSKA.
Pellegrini said: “I think both clubs have the same pressure. It is a big thing here in Italy, they have spent a lot of money on different players and have a very good squad. I think the pressure for both clubs is exactly the same.”
As well as being without Aguero, City are again missing key midfielder Yaya Toure through suspension.
The positive news is that playmaker David Silva, out since October with a knee injury, and captain Vincent Kompany, who has missed two games with a hamstring problem, have both trained and could return.
Striker Stevan Jovetic, who was rested against Everton as a precaution against a hamstring niggle, could also feature – although Pellegrini was coy when asked about the trio.
He said: “All of them could be ready. There is some doubt about one of them but we will see tomorrow.”
Pellegrini admitted it has been a troubled group campaign but he is confident of a positive outcome.
He said: “Maybe we made a lot of different mistakes in the other games, especially against the Russian team, but we have a chance.
“As we demonstrated against Bayern Munich (in a 3-2 win last time out), we will fight to qualify. Tomorrow we will try to do it. I am sure we are going to do it if we play a very good game.”