Incomplete seating of the cartridge or incomplete depression of the stem, caused by contamination or by wear in the parts you didn't replace.

Did you flush out the system with a minute or so of water before you put the new cartridge in? Grit, scale, or fragments of old O-rings can prevent a good seal from happening. To flush the system, turn a glass or a bucket upside down over the disassembled faucet and turn the water back on. Have a towel handy.

If it still drips after that, the next question is whether the cartridge itself is leaking, or whether it's just not being closed all the way. Turn the water off again, disassemble things again to the point where you can see the cartridge but don't remove the cartridge. Push the stem down by hand, this won't take any real force. Turn the water back on.

If it's stopped dripping with the stem pushed down by hand, the problem is the connection between the lever and the valve stem. This involves plastic parts that can wear. Make yet another trip to the hardware store with the old lever and plastic cap. Buy at least the plastic cap. Put it on, pull the lever up, push the lever back down.

If it's stopped dripping with the new plastic cap, you're done. If it's still dripping at this point, the retaining nut that you unscrewed to get at the cartridge may be the problem. Turn the water off again, disassemble things again, remove the retaining nut. Make yet another trip again to the hardware store, buy a matching retaining nut, and use it as you reassemble things yet again.

If it's stopped dripping with the new retaining nut, you're done. If it's still dripping, make sure the decorative cap over the plastic cap is fully seated. It turns out to be more than decorative.