Alvaro Negredo scored a hat-trick following Sergio Aguero's early brace as City hammered CSKA Moscow 5-2 at home to advance to the last 16 with two games to spare.
However, City still trail group leaders Bayern Munich by three points after the holders maintained their 100 per cent record with a 1-0 win away to Viktoria Plzen.
The odds are against City finishing top of the group and Pellegrini is making no predictions as to how far his team can go in the tournament.
"It's the first step," Pellegrini told Sky Sports. "This is what the club wanted to do for the last two years, so our first target was to qualify for the round of 16.
"The most important thing today is that we can now play the last two games of the group thinking about trying to be the first in the group.
"After that, we will see the draw and see in February.
"It's very difficult to know [how far City can go]. I think everything can happen in the knock-out stage.
"The team we will play against will [probably] be the first in the group, so that will be very difficult."
Fernandinho and David Silva were both substituted due to injury and Pellegrini confirmed the duo will be assessed on Wednesday.
The City boss added: "David Silva and Fernandinho both had to be substituted. They have small problems, so we'll see tomorrow with the doctor."