Too funny! While studying in Basel I once participated in a seminar (in German of course) where Greek was used. What I pronounced as a theta became a teta in the mouths of my fellow students. And if you should ever study biblical Hebrew, have fun trying to pronounce the gutturals (aleph and ayin)!
The bottom line is that pronunciation is a physical exercise. It takes lots of intentional repetition to build muscle memory. Try to imitate everything: the intonation, the emotion, the body language, even the facial expressions. Slight deviation in pronunciation is no big deal. In fact, not all native speakers of a language will speak in exactly the same way. In Hawaiian, for example, the letter"w" can be pronounced as a "w" or as a "v" and will be pronounced differently by Hawaiians growing up in different parts of the islands. Also, don't be ashamed to pronounce loan words from, say, German with an American pronunciation. Purists will insist we say Adidas or Porsche "correctly," but the truth is that the "American" pronunciations are how the companies advertise their names in America.
If you're studying New Testament Greek, you will need to decide which system of pronunciation you want to use. The same goes for Latin. Whichever system you decide on, try to master it. Your professor may quiz you over it! (Which is the point of this blog post.)