The situation is similar in Australian Universities as well. Most of them will be fine with a 3 year degree but there could be some which are reluctant. I will suggest you to look at the Prospective Students > Requirements or Eligibility column (or something similar) of the universities that you want to apply. I will be very surprised if good universities have these strict restrictions.
What about Australian universities ??
There are a few number of universities that will be reluctant to accept you. However, the good universities will be very flexible and will allow you different ways to prove your competency. In the US, you are required to do GRE. It can be proved to show your competency. Also, majority of the time, they will care more about the specific courses you have taken. For example, if you are applying to study Maths in Masters, you need to prove that you are comfortable in Maths by showing them the number of Maths classes you have taken and your GRE scores.
In conclusion, if you have the opportunity then go for a four year degree but if you can’t you might have to do a little bit more work while applying to certain universities. I will suggest you to look at the Prospective Students > Requirements or Eligibility column (or something similar) of the universities that you want to apply. That might help you decide. Best of luck and feel free to ask a follow up question.