City fought from behind to lead 2-1 in the closing minutes, only to get caught on the break in the 90th-minute and concede an equaliser.
The champions are now 13 points behind Liverpool, who also have two games in hand over the champions.
“We tried to do everything,” said the City boss.
“The spirit was there. We tried and tried. We came back and it’s a pity we dropped points like that. But it’s football.
“We struggled a little bit in the first 10 minutes of the second half. We came back without thinking too much what we have to do.
“I think we did everything. We attacked, put many crosses and corners into the box. They didn’t do much, but they get a point.
“We knew it would be hard. Last season when they beat us it was the same.
“They had two, three chances and scored. In general we controlled the games against them, but you have to avoid mistakes.
“You should not allow Zaha to run at you, but we did and after we concede a goal.”
Asked if he had used a more familiar formation against Palace, Pep said: “No, today we played similar to the way we did at Aston Villa, with Mendy attacking down the left and players in the middle.”
On the overturned penalty decision, Pep said: “I don’t know the rule on the hands. It looks like hands but… “
And on the inevitable title race question, the Catalan responded: “Maybe I will watch Sheffield United, I don’t know. I have answered this question many times.”