Releasing a piece of software as not beta should only be done after testing. You will lose most of your customers, when only one GUI element is not working. For example, a well known online clothing company (I don't know if I'm allowed to write down the name) released an update to their Website which doesn't allow chrome users to access their shopping cart by mistake. Imagine: you have done all your shopping and then you get mad, because you can't buy your items. You will then never go back to that website.

I would recommend, that you talk to your boss. And if that doesn't help, ensure, that you don't get held responsible for any caused damage.