Pellegrini: Top spot not Man City's main aim
City recorded a 4-2 triumph over winless Viktoria Plzen on Wednesday, moving them three points behind the Germans, who they face in their final group game in Munich.
Pellegrini knows his men face a tough challenge to dislodge the defending champions at the summit, with City needing to better the 3-1 result that Bayern achieved at the Etihad Stadium.
However, the Chilean is happy just to be in the final 16 and is now more concerned about the visit of Arsenal in the Premier League, which comes just four days after the trip to the Allianz Arena.
"I think for the moment the Premier League (is the priority)," he told Sky Sports. "We are going to play in Munich, we will try to win, but winning 3-0 in Bayern is not easy.
"It's important, but more important is the next game when we play Arsenal."
Pellegrini's side continued their excellent scoring run at home, with 40 goals coming in their last nine games at the Etihad, but they have shipped two goals or more in each of their five group games.
And he conceded that there remains room for improvement.
He added: "Always when our team concede goals is a concern for me, because we are not doing something well.
"Today Plzen scored two goals and had two or three more chances. Last game CSKA scored (twice). It's important also to score, but we must continue to improve."
Sergio Aguero was withdrawn at half-time but Pellegrini confirmed that was always the plan, dismissing any suggestions of an injury to the Argentina international.