Had City, who lost 1-3 at home to Bayern in October, scored a fourth goal in the Allianz Arena, and held on to their lead, then they would have won their group.
Yet with two minutes remaining Pellegrini withdrew striker Edin Džeko for holding midfielder Jack Rodwell, and appeared to confirm he was not aware City could have topped their group on the head-to-head ruling.
City needed one more goal to win Group D and avoid a seed
Asked why he did not bring on striker Sergio Agüero, instead, Pellegrini said: "I was tempted if we scored the fourth goal."
"It was important to be first in the group but not the most important. It was difficult to score two goals."
Midfielder James Milner, who scored the winner, admitted the players thought they needed to win by three clear goals due to the goal difference deficit.
“We didn’t know if 4-2 would be enough or if we would need 5-2," Milner revealed. "We thought it needed to be 5-2 to be honest. It’s not easy to score three goals here, so to score four would have been a tough task. It’s pleasing to score three goals at a place like this and we’re going to need to do that in the next round.
“We’re slightly disappointed we did not finish top of the group. But to be slightly disappointed at beating Bayern Munich in their own ground is pretty pleasing.”
Pellegrini's blunder is similar to former City boss Alan Ball's costly error on the final day of the 1995-96 season, during City's 2-2 draw with Liverpool at Maine Road.
Ball instructed his City players, bidding to avoid relegation, to keep the ball by the corner flag in a bid to kill time after he had been told, incorrectly, fellow relegation rivals Southampton had gone behind at home against Wimbledon.
Tragicomically, the substituted Niall Quinn, who was watching the scores on a TV in the tunnel, burst out onto the touchline and informed his teammates they needed another goal. It never came and City were relegated.
City's second-place finish behind Bayern means they will be drawn against a top seed in the last-16 draw on Monday. They could potentially face Real Madrid, Barcelona or Paris Saint-Germain.