You're not unreasonable to feel sad.
Often, our lives do not turn out how we imagined them to.
It's OK to feel sad about that.
And you're right, we're not all born with equal access to resources. There are things I want and need, even, that I don't have access to, and am not likely to ever access. For example, I cannot see a path for me to secure housing. It sucks.
However...(you knew that was coming, didn't you?!) While I am still alive, I do try to count my blessings. On a really bad day, my blessings are that I have running water and a flushing indoor loo. On better days, my ability to have my own children, to hold down a (poorly paid, relatively low status but congenial) job, to have sight and hearing to see and hear nature around me, to have access to books and music.
It really does help me sometimes to acknowledge the sadness, yes, but then also acknowledge the things I have that others around the world don't.
There is a real opportunity for you to be a real role model for your kids. Acknowledging and getting effective treatment for mental health issues - that's being a good role model, for starters. You work - that's another example of good role modelling. If you hug your kids, have their back, show them how to get up and live to fight the next battle - that's being a good role model.
Look, I do get it. I have cried some very bitter tears about what I've not been able to give my kids, because of (childhood abuse driven) choices I made earlier in my life, and because sometimes the cookie just crumbles that way.
Feel sad. But sometimes take stock of what you do have, and allow yourself to feel grateful for it, and acknowledge the good parts of your parenting and your self. If you can't do it (and I couldn't either) therapy with someone skilled (and again, I know it's so unfair - if you had money, you could pay for this privately, as it is you're on waiting lists, most likely) can really help you be able to acknowledge, access and build on your strengths, and not remain bogged down in what you perceive as your failures and weaknesses.