This isn't necessarily a very difficult problem to fix, but I thought it was a bit confusing with these old MOEN kitchen faucets. This particular faucet is about 22 years old. It has a U-shaped black plastic thing underneath, which at first I thought was missing some screws and thought the missing screws were the reason the thing was loose. However, that is not the problem at all.
The real thing you need to tighten is the bronze nut that is directly in contact with the U-shaped metal part. Likely it will be difficult to tighten this nut. An adjusting wrench will likely be too big in size. I found that with a lot of difficulty I was able to tighten this nut using the most basic box wrench, 1/6th of a rotation at a time! It took me about 10 minutes to tighten this way but all is well now. Apparently plumbers have special wrenches that are much easier to use for things like this, the wrenches that reach up with an extended vertical arm and in tight spaces. I didn't have one, most people don't have them.