Importing Blender object with animation to Unity

Hey!
I am trying to create a plant-like object that is animated to look like it’s growing. I found this tutorial: https://www.youtube.com/watch?v=FdEAx3SbFaw

I want to create the object and the animation in Blender and then use it in a Unity project. The Blender part works fine but when I import the file into my Unity project I can’t get the animation to work there. I’ve tried with both .blender and .fbx files and neither work. The animation window in Unity shows up in the Inspector with the right amount of frames but there is no movement.

I’m a beginner with both Blender and Unity, using Blender 2.75a and Unity 5.1.3f1 Personal.

Thanks!

Unity will import the bevelled curve as a mesh so you will lose all the animation you have made by changing the curves