Play secret of mana or zombies ate my neighbors on wii U?

Because those games are on the Wii Virtual Console, they require some kind of controller that the Wii (not the Wii U) knows about - the system is operating without access to any of the Wii U specific stuff when you're doing this.

That means you need either a GameCube controller, or a Classic Controller attachment for a Wii Remote - and since a Wii U doesn't have any way to plug in a GameCube controller*, that only leaves the actual Classic Controller.

You can still use the Pro controller for Wii U games that support it, but for Wii content, it can't be done.

While the recently released GameCube Controller Adapter does allow you to attach GameCube controllers to your Wii U, the adapter is currently only compatible with Super Smash Bros. for Wii U - it is not supported in Wii mode.