To produce a Japanese R takes a bit of practice. But as starting tips, you should not be trying to say R, you should be trying to say D. But not a D with the top of your tongue, and certainly not with the tongue against the teeth like in some languages; it should be a fast D with the tip of the tongue. The R sound only comes about from the vowel-like features of this; don’t try to do anything with the back of your mouth. This will also sound like an L if you let air escape around the tongue, hence why it sounds similar to people who speak a language with nothing else that comes close—in Korean, which has basically the same R sound, there is a fairly regular L sound, but it is mentally treated as a longer R sound.
There is no such thing as a “real R”; it is completely dependent on the language, and there are about five or six different ones in common use among languages that use the Latin alphabet. One of them, used in Iberian and Italian languages, is about the same as in Japanese, but there is no confusion with L because the L sound remains an important distinction in those languages.