A 66th-minute strike by Bosnian Edin Dzeko settled a closely-fought match in which England goalkeeper Joe Hart made a string of good saves to help extend City's home league record to 10 wins out of 10 and send them top of the table.
But after scoring 37 goals in nine effervescent home games, it was a flat display from City who moved two points clear of Arsenal, who play on Sunday.
"I think the team that wants to win the title must have different faces," Pellegrini told reporters. "We usually score lots of goals at home, but after 45 minutes we knew it would not be like that."
Pellegrini made six changes to the side that beat Liverpool 2-1 on Thursday and was as frustrated as his players and the crowd as they struggled to break down a stubborn Palace defence.
"Of course I was very concerned," he told Sky Sports. "Before the match, I said when we finished against Liverpool, 48 hours ... it is impossible to recover for players.
"We didn't have our team fresh and it is very difficult when just one team want to play and the other just wants to defend. So, that was the game we saw today. That is not what we are used to do at the Etihad."
Pellegrini also played down fears an eye injury suffered by Hart when he came out to challenge Palace striker Cameron Jerome.
"Yes, he has a cut in his eye, but he never had any problem," said Pellegrini, who on Friday had declared Hart to be 'the best goalkeeper in England' having dropped him two months earlier.
The Chilean also distanced himself from any suggestions that his team would now stroll to the title.
"I repeat, there are six or seven teams that will continue fighting for the title to the end," he said.
"Of the last eight games, we have won seven and drawn one and recovered the distance Arsenal had on our team, but we continue next Wednesday (at Swansea) and the second half of the season will be very difficult for all of us."
Crystal Palace manager Tony Pulis, who watched his team haul themselves out of the bottom three with a 1-0 win at Aston Villa on Thursday, bemoaned the fact they could not deliver a repeat.
"We are really disappointed not to have taken anything from the game," he said. "The difference between the teams is spending about 350 million (pounds).
"The weekly wages of one of their players would probably cover half my team and, if I was their manager, I would be sat on the sidelines with a cigar in my mouth.
"I think Joe Hart made a couple of great saves today and you know that when you come to places like here, you are going to come under pressure - but we looked dangerous on the break."