Bayern winger Arjen Robben, who scored their third goal, said he had anticipated more from their big-spending opponents whose squad is packed with talented international players as they seek to be serious domestic and continental contenders.
"We were so dominant against such a big team in Europe - I think we also didn't expect an easy game like that," he said. "I think it's a big compliment to our team, but I also expected a little bit more from City.
"We didn't give them any space, we pressed them forwards. Sometimes they gave us a little bit too much space, and I think we are a team that can use the space very well.
"City weren't as organised defensively as we had expected and we used the space they offered us clinically. There were some attacks of ours that simply were fantastically executed."
His manager Pep Guardiola said it was disrespectful to call it an easy game but the statistics of 61 per cent possession to 39 per cent and 13 attempts on target to two tell a different story.
"What happened today (was) we played better, we played good, we won," the Spaniard said.
An early goal by Franck Ribery and second-half efforts from Thomas Mueller and Robben gave Bayern the victory but there were plenty of other wasted chances that meant the scoreline could have been far worse for City.
The hosts' keeper Joe Hart had much to answer for with the first and third goals on a night to forget for the England international as he was beaten first by a low effort that was not as powerful as it could have been and then at his near post.
Pellegrini, in contrast to predecessor Roberto Mancini who often singled out underperformers for public criticism, refused to blame the man wearing the number one shirt.
"Of course the three goals we can do it better, all of us, not only the keeper," he said.
"I am worried about the mistakes but I think that this was not an easy game, we played a strong team, our performance was not the way we (we have been) playing (in other games)."
City, whose only other Champions League campaigns have ended with group-stage exits in the past two seasons, are desperate to make an impression on the European stage after splashing nearly £100 million on new players in the close season.
They are second in the group with three points after two matches, with Bayern leading the way with a maximum six and CSKA Moscow on the same points as the English club. Czech side Viktoria Plzen are bottom, having lost both of their games.
Pellegrini knows that while this was just one game, his team have to improve on all fronts if they want to succeed in Europe.
"The difference between City and Bayern can't be the difference you saw today," the Chilean said.
Former Barcelona manager Guardiola said that despite the heavy defeat that took his record against former La Liga rival Pellegrini to eight wins and a draw in their nine encounters, he still believed City would qualify for the knockout stages.
Despite his obvious delight at what he agreed was their best performance of the season, the Spaniard said his side had plenty of room for improvement.
"Our (set-piece) plays were catastrophic, terrible, we have to improve that," he said. "We have to defend well in our zone defence.
"I am very, very, happy but it's not the final of the Champions League, it's just the second game, we have time to improve and recover players and make little steps forward."