What your teacher meant is that you just need to try USING English first and not analyse it too much. S/he is not telling you to ignore them. You will naturally make mistakes, but never ignore them. Look back at what you have done wrong (and have done right!) and learn from that. Here's a correction of what you wrote, See what you can learn from this: My English teacher always says, "Learning English is a piece of cake. Don't worry about pronunciation. Don't worry about grammar. Don't be afraid of making mistakes." Yet I don't see my own progress. Have I not worked hard enough or am I learning English the wrong way?"

English is a very simple language just as simple as Chinese

I agree with Peachey. I think your teacher is trying to encourage you to enjoy speaking English. If you weren't learning anything then you wouldn't be able to communicate on italki! :) Believe in yourself, it will happen without you knowing it!