Leaky Connection: Plastic tubing to Water Inlet Valve

My Problem/Question:

I’m having a problem properly sealing the connection between the water inlet valve and the plastic tubing with the plastic nut. It’s an Amana 22 (Model No. TLI22KL) refrigerator. My water inlet tube cracked…I’ve replaced the tubing but I am having a problem properly sealing the tubes connection to the water valve inlet. I don’t seem to have a compression fitting that slips over the tubing (new tubing didn’t come with one either). When I removed the defective tube there wasn’t a compression fitting, just a spring in the tube.

Can you tell me if I need to purchase a compression fitting to seal the connection?

If so, do you know where I might be able to purchase it?

Or, should the tubing somehow seal itself in the plastic nut?

Abbie’s answer to similar question I found:

You can buy a brass 1/4 inch coupler at Lowe’s. It comes with two brass compression washers. Slip the brass compression nut in the tube and then the brass compression washer, then install. After installiation, pull on the tubing to make sure the plastic water line is captured and won’t come out.
Also, a new universal water valve comes with steel sleeves that get inserted in the water line to help the compression washer dig into the line better. I don’t know where you can get these, but You can check with this parts site to get everything. It is best to use these as the inlet water pressure is the same as the house, rather high.