City went top of the Premier League thanks to Edin Dzeko's 66th-minute strike - his 50th for the club - as the hosts sealed a hard-fought win over resilient Palace, who are scrapping for their lives at the opposite end of the table.
The result maintained City's perfect home league record this season, making it 10 wins from 10 at Etihad Stadium, although it was a far cry from the thrashings handed out to the likes of Norwich City, Tottenham and Arsenal in recent weeks.
While delighted to make it nine wins from the last 10 games in all competitions, Pellegrini accused Palace of being too negative.
"We knew it was going to be difficult," he said.
"It's difficult when just one team wants to play but I understand why they do it.
"It's impossible to play 44 hours after the sort of game we had against Liverpool and we knew our team would not be fresh, so it's very important to know how to win 1-0.
"One team wanted to play the 90 minutes and the other just wanted to stay in their own half.
"Our team was not fresh enough to make the movements you have to do when you have 10 players on the edge of the box."
City now sit two points clear of Arsenal at the top of the table, with Arsene Wenger's men travelling to Newcastle United on Sunday.
Pellegrini added: "We know we are top at the moment and that's where we wanted to be.
"We are still in all competitions, we are top of the table and maybe eight games ago nobody believed that we could be.
"We must continue this way but it's only halfway and the second half will be exactly the same with five or six teams fighting for the title until the end."
