Lighting, Light Fixtures, Ceiling and Exhaust Fans - Extra ground wire

I just replaced an old light/exhaust fan in my bathroom and just wanted to make sure that my wire connections are safe. My house wires only included:
1 Black
1 Red
1 White

The new light fan has
2 black
2 white
1 green

My connections were as follows:
1 house black with 1 black wire from fixture
1 house red with 1 black wire from fixture
1 house white with 2 white wires from fixture.

My main question is what to do with the green (ground) wire that came attached to the new fixture. Since my house wiring did not have a ground wire I simply tucked the green ground wire in the metal housing of the new fixture (only connected on one end).

The light and fan are working properly but Ii just wanted to make sure it is a safe way to handle the green ground.

Thanks

A grounded fixture is safer than an ungrounded fixture, but if your house does not include grounding, there's only so much you can do. If your house is wired with metalic conduit and metal boxes, you should connect your fixture grounding wire to the metal box. Otherwise what you did is the best you can do.