I agree with Debby that one very powerful way to let go is to pack it up in a box and leave it for months. Then if you do have that regret - go into the box and get whatever it is you're remembering.
Another idea is, if it is a sentimental item, take a picture of it to remember it by.
The hardest part is to let go of what I (and others LOL) call the "poverty mentality." That is, the thought that, "What if I need this some day in the future because I'm totally broke, need one, and can't afford to buy it?" I personally have countered that in myself with this line of thought: how much energy am I spending every single day to maintain all this stuff? How much more energy and time would it free up to not be tripping over boxes of stuff I don't use? I also, like Debby, think about how fortunate I am to have the problem of having "too much stuff" and how great it feels to pass on useful things to people who really need them.
What type of items do you think about most after you get rid of them? Think about it and try to analyze *why* those items in particular are so hard to let go of. This might help. You also might choose to keep those things, and just keep them well-organized so you really can access and use them. But it will be a lot easier without twenty other unused things around them in the box.
Good luck. It isn't easy...definitely a process, and you're doing great to be examining what goes on with you when you get rid of things, and why.