The new cartridges come with a plastic "key" that you are supposed to use after pulling the retaining clip but before attempting to remove the cartridge. This loosens the barrel/sleeve to help ensure that it comes out when you pull.
Since you did not use it (or you did but the barrel/sleeve still got stuck), you will likely need to rent or buy a special puller tool. The good ones are expensive ($80) to buy but good plumbing shops rent them. Ask around plumbing and hardware shops (not the "big box" stores) to find somewhere that rents a "Moen Puller". Mine looks like this:
I'm replacing an ancient Moen shower cartridge at my girlfriend's house and I'm stuck. I got the old one out surprisingly easily and the new one (#1225) slid right in. However, I can't manage to get the flat brass locking pin (kind with two legs) to slide in to lock the cartridge in place. It feels like I'm getting solid resistance on both sides despite having lined the notches up as carefully as possible and making sure the new cartridge is seated all the way in. It almost feels as if the new cartridge is a mm or so longer than the old one.
I'm considering using a file or hacksaw blade to widen the slot for the locking pin a little. Any other ideas?