There is probably some hard water deposits inside the valve where the cartridge O rings and seal make contact. The slightest deposit will break the seal and you'll have a drip. Get some fine emery paper and gently clean out the valve making sure it's totally smooth inside. Then get some plumber's grease, coat the cartridge and reinstall. Hopefully you didn't damage the O rings inserting the cartridge the first time.
Answer from JACK on Stack Exchangeplumbing - Moen two handle bathroom faucet - new cartridges but still drip - Home Improvement Stack Exchange
Need to lubricate Moen faucet every 3 months! - Bogleheads.org
Replacing cartridge in Moen double handle bathroom sink
Moen bathroom faucet handle replacement
Videos
There is probably some hard water deposits inside the valve where the cartridge O rings and seal make contact. The slightest deposit will break the seal and you'll have a drip. Get some fine emery paper and gently clean out the valve making sure it's totally smooth inside. Then get some plumber's grease, coat the cartridge and reinstall. Hopefully you didn't damage the O rings inserting the cartridge the first time.
It's most likely the valve body