I have a number of faucets of a similar style and you will want to check and replace the seat. In the image below, the seat is the little threaded part at the bottom. It's placed behind the cartridge (contrary to how it's shown in the image)
You'll need a seat wrench to get it out:
Likely you will find that there are notches in it. Get a replacement and screw it back in firmly. Do not use pipe dope or Teflon tape (thanks @JimStewart.) It should go in easily if it's in the right position. You don't want to cross threads here.
They should have seats where you bought the cartridge. Take the old seat in to make sure you get the right one. I'd buy a handful. You will probably be doing this again before long.
One problem I have run into with replacement cartridges is that they use a rubber gasket instead of the felt ones in the original cartridges. After the cartridge is tightened, this gasket is compressed against the shaft and as the faucet is opened and closed, the gasket turned with it and caused the assembly to come loose. This might not be an issue with this design but to solve that problem, I used a little plumbing grease on the shaft to allow it to turn without moving the gasket.