Edin Dzeko’s 50th goal for the club earned City its fourth consecutive league win under the Chilean for the first time, sending it to the top of the table, with Arsenal playing on Sunday.
Palace was a threat throughout, but when asked if City was fortunate in victory, Pellegrini insisted a 1-0 win after playing less than 48 hours ago was admirable - especially against a team he deemed to be very defensive-minded.
"No, I don’t think we were fortunate to win the game today," he told reporters.
"I was absolutely sure before the game that it would be very difficult, the team was not fresh so it would be very difficult game. That is why it is important to know how to win 1-0.
"We were absolutely sure that we were not going to have an easy game today against Crystal Palace; it’s very difficult when only one team wants to play and the other doesn't, I understand the way they [Palace] do it, but our team was not fresh enough."
Joe Hart was named man of the match after denying Palace a number of key opportunities, and Pellegrini claims the England international’s form is thanks to a much-required stint on the sidelines.
"I think it was good for Joe to have a rest - he needed a rest," said Pellegrini. "He’s playing at his normal performance and he’s playing as the good goalkeeper he is.
"I don’t think that he has less confidence, he always knew what we knew about him; he needed a rest, it was hard, but he always knew he would return to his position."