You are not being unreasonable for feeling upset, but it does sound as if your employer had the right to dismiss you.
Quite a few people on here are suggesting you appeal the decision, but I'm not sure that's a good idea in your circumstances. Doing so is likely to be stressful and unsuccessful.
Think very carefully about taking any action that might lead a an employment tribunal. From what you have told us, the union will not support your claim and your employer will throw the kitchen sink at defending it.
The process is time-consuming, often drawn out over several years and absolutely brutal. Even if you represent yourself, it can be very expensive because you need to cover all your expenses, time off work, travel, preparing bundles, printing, etc.
Despite what we read and hear in the news about people winning large sums of money, ET cases they are extremely difficult for employees to win. If your case is deemed by the tribunal to have no merit, they can award costs against you which can go into six figures if your employer is using expensive lawyers (which they will).
I have been through the process and it dominated over two years of my life and nearly broke me. I took legal advice before proceeding and was advised that my case was good enough that I could still win even without representation in the tribunal hearing (I couldn't afford a barrister).
Although I won a small part of my claim I was only awarded three months pay. I substantially lost my case. I spent considerably more on making my claim than I was awarded by the tribunal, despite having no legal representation during the hearing.
It is very unfair if you have been treated badly by your employer, but it is only worth making a ET claim if you have a water-tight case, nerves of steel and very deep pockets.