Cyanoacrylate glue, commonly known as "superglue" will bond nearly any two types of material together. Usually it's thin enough to be pulled by capillary action into the thin space between two parts that have already been assembled. You simply put the plastic thingy into the metal whatsits then put a drop or two of glue on the joint line. The glue should disappear into the joint and it'll set in a matter of seconds and you'll be good to go.
You do not want to put too much glue in there - you literally only want one or two drops! If you can still see the glue at the joint line you've got too much. If you do get too much it will take forever to cure and you'll end up with it gluing your fingers on as well. You can get your fingers off by pulling. You'll pull skin off and it'll likely hurt, but you'll survive. If you move quickly, you'll get a bit on your fingers but get your fingers off before they're glued in place. Now you'll have some on your fingers and it'll wear off in a day or two of general living.
Purchase a package of very small, single use tubes. The stuff invariably dries and hardens at the tip of the tube once you've opened it, and just about nothing will reopen the tube, so even the industrial size tubes end up being "single use". May as well start out planning on throwing it out after the one use.
If you need to apply the adhesive before assembling the parts, you probably want to use epoxy to join two dissimilar materials like plastic and stainless steel. (You sure it's actually stainless and not galvanized or zinc coated?) Check the labeling on the package you're considering purchasing - most of the ones I've seen will contain a little matrix of materials with an indicator showing whether it will or will not work on any particular combination.
For small use, you'll probably end up with a small, dual-syringe dispenser. One push will expel the correct amount of resin and hardener. Squeeze it out onto a piece of scrap cardboard, wood, or other disposable surface. Use a stick (or the provided stirrer) to mix it thoroughly, then slather a bit on the plastic thingy and gently push it into your metal whatsits. Wipe off any excess and set it on a piece of wax paper to dry.
Be sure to read the instructions that come with the epoxy to ensure you've mixed your particular kind properly and to see what the setting time is. Don't use it until it's fully set.