No you haven't. But, you should probably let it warm up to the recommended temperature, let it finish fermenting and then switch to fermenting ales for a while. It ought to still ferment fully and be drinkable, but it won't taste anything like what you might expect a lager to taste like.
Lagers are really much more difficult to produce well than ales due to the different physiological needs of the lager yeast. The lower fermentation temp. requires pitching much more yeast than is normal for ales, and you really need good temperature control, among other things. If you ferment at a lower temp without making sure you're pitching and managing the fermentation correctly, you're not going to end up with a better tasting lager, in fact you'll probably end up with something rather disappointing.
I think lagers are generally a bad place to start homebrewing because the work/worry/complexity-to-reward ratio is just too high. It's kind of like trying to learn calculus before you learn algebra. Ales will give you much better results in a much wider range of fermentation temperatures with much less fuss and a huge deal less to go wrong. I'd suggest getting a bunch of ales under your belt before you dive back into the lager scene.
Looks like you're actually already fermenting with ale yeast. They really ought to put the word 'lager' in quotes...