That stuff should have PSA on it......were you able to apply heat and pressure? Usually, we heat to about 100 F or so to get the stuff to adhere. The cloth is probably not good enough surface to make good contact since the individual threads are relatively loose and pull away.

Is there a way to use the sticky to adhere the strip to a plastic push-in button? You could push the Christmas tree into the door panel thru the cloth and used the flat face of the Christmas tree to stick the chrome to.....but then, you would have to have a row of closely-spaced insert trees. Next thought....can you screw a strip of aluminum to the door thru the cloth....the aluminum strip is thin and about as wide as the chrome.....then stick the chrome to the aluminum....hidden screws.