Copying the files to your plugin directory was the correct thing to do, since the installer won't work on x64. But assuming you're running the 64bit version of Firefox, you can't just expect the 32bit plugins to run directly.
You need to install nspluginwrapper first. Then you have to enable the plugin to run through it by entering the following command:
nspluginwrapper -i /<pathtoplugin>/libflashplayer.so
It should work after that.
Actually, I believe you can install flashplayer to just about anywhere on your system. It doesn't have to be in your plugins folder. Just direct the pathname above to wherever you placed the files.
For more on 64bit plugins, see here:
Firefox PluginDoc (Linux x86-64)