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Mindfulness practitioners talk a lot about letting go, but “just let it go” can sound like facile advice that doesn’t acknowledge how difficult things are for you or how much you’re suffering. Besides, how are you supposed to just forget about your problems, anyway? As if pretending they’re not there will make you feel better. 
And you’re right, ignoring problems doesn’t help. But, it turns out that’s not what letting go is all about.
Letting go does not mean getting rid of. It means letting be. 
We’ve talked before about the two kinds of suffering. Primary suffering is caused directly by what’s happening to you. If you sprain your ankle, suffering comes in the form of pain. Secondary suffering comes from your reactions to what’s happening to you. Maybe you feel sorry for yourself because you’re in pain, or you feel agitated because you have to wait for treatment, or you lament the fact that you won’t be able to go for a walk for a while. Letting go helps you directly manage that secondary suffering.
To let go is to first acknowledge the reality of what’s happening as well as your reactions to what’s happening, then relax into and release your reactions. So, it doesn’t mean ignoring or escaping from the conditions and challenges of life. It means facing them, even embracing them. Letting go properly results in less suffering and more happiness and peace.
Letting go involves trusting in your ability to manage and cope. In his book, Shambala: The Sacred Path of the Warrior, Chogyam Trungpa offers this example: 

Obviously, letting go is more than just relaxation. It is relaxation based on being in tune with the environment, the world. One of the important principles of letting go is living in the challenge. But this does not mean living with a constant crisis. For example, suppose your banker calls and says that your account is overdrawn, and the same day your landlord tells you that you are about to be evicted for failing to pay your rent. To respond to this crisis, you get on the telephone and call all your friends to see if you can borrow enough money to avert the crisis. Living in the challenge is not based on responding to extraordinary demands that you have created for yourself by failing to relate to the details of your life... When you let go properly, you can relax and enjoy the challenge (p. 77).

Let me give you another example, one we can all relate to right now. The threat of COVID-19 can cause anxiety and letting go can help you release that anxiety, which is a form of secondary suffering. But, you have to let go in the right way. Heading out to a party where you’re in close proximity to other people is a reckless, irresponsible way to try to relieve anxiety. It amounts to ignoring the problem or pretending the problem cannot affect you. That’s not what we mean by letting go. 
Letting go looks different. It includes accepting your potential role in spreading infection and responding by washing your hands, staying at home when you can, distancing yourself from others, and taking all the other precautions recommended by experts. When you face challenges in a thoughtful, logical, responsible way, you are free to relax into the situation. You can begin to feel happy and peaceful.
And these forms of happiness and contentment are not artificial. It’s not you trying to trick yourself into cheering up. It’s a genuine feeling generated from being at peace with whatever is happening in life and confident in your ability to cope. It is resilience itself.
But, you say, even if I take all the actions I can to avoid negative consequences, bad things can still happen. Yes, they can. Letting go also involves an acceptance that you cannot control everything.