Edin Dzeko scored the only goal of the game at Etihad Stadium as the struggling Eagles gave as good as they got.
"We are disappointed. It was always going to be a tough game, playing the second away game in a few days, and coming to Man City who are the form team in the Premier League, it was always going to be a tough ask and a tough challenge.
"The players went about their business very well.
"We looked very solid, the shape was good and we looked dangerous on the break.
"It is just about picking that final pass or finishing off the opportunities."
After pinching a 1-0 win with an injury-time Dwight Gayle strike at Aston Villa, Pulis admitted his side needed to squeeze as many points from close games as they can to avoid the drop.
Pulis said: "We have gone away and done well. What we need to do is turn 1-0 defeats into draws if we can or even victories.
"It will be tight but we are in the group now which is something we weren't when I came.
"If we can bring a few players in and strengthen it up a little bit we can give it a good blast when the year turns round."
Pulis confirmed Jerome suffered an ankle injury in a clash with Joe Hart - which ended his involvement - and will be assessed in the coming days.