I suspect you have a 2G iPod. Those can only go to iOS 4.2.1.
iPod touch (3rd generation)
iPod touch (3rd generation) features a 3.5-inch (diagonal) widescreen multi-touch display and 32 GB or 64 GB flash drive. You can browse the web with Safari and watch YouTube videos with Wi-Fi. You can also search, preview, and buy songs from the iTunes Wi-Fi Music Store on iPod touch.
The iPod touch (3rd generation) can be distinguished from iPod touch (2nd generation) by looking at the back of the device. In the text below the engraving, look for the model number. iPod touch (2nd generation) is model A1288, and iPod touch (3rd generation) is model A1318.
It is just not powerful enough. The 1st and 2nd gen iPod Touchs have 128MB of RAM. And much slower CPUs.
I have a 2 year old 4th gen with 256MB of RAM and a slower processor than the 5th gen, and I can tell you that the 4th gen is hurting at iOS 5. I have apps now that will not run because there is not enough RAM. I've avoided going to iOS 6 because it demands even more resources, and I figure I'll start having more problems with apps not running correctly.
I understand that the handheld mobile device market is moving very quickly and hardware is advancing very quickly and the software is pushing the boundaries. Today's devices could not be built 4 years ago. Using 4 year old technology to give today performance would have made a device much bigger, use battery faster, generate a lot more heat, and cost a great deal more. And if they actually did that, and people actually purchased it, the software could have pushed it boundaries, and more powerful units would still be made today and could run on older equipment anyway. It is just the nature of mobile device hardware.
It's not just RAM, it's also the fact that certain apps simply use newer features that the older iOS devices didn't/don't have. For example, higher end OpenGL, digital compass, accelerometer, etc.
I used to own an iOS device that could only be updated to iOS 4.2X and so I found myself in the same situation as you're in now with all the new apps unavailable to me and with some of my old apps telling me that my device will be unsupported in coming app updates.
There is, unfortunately, no workaround in terms of getting new apps on the device and being able to utilize them, HOWEVER, if you see apps that you would like to have, you can still purchase them and download them using your computer's iTunes program and then save them to port over/transfer later if you end up getting yourself a newer iOS device.
This is what I did for the last few months before I received my new device as a gift.