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.
To more easily find compatible apps:
iOSSearch - search the iTunes store for compatible apps.
Apple Club - filter apps by iOS version.
Starting when iOS 7 was released, Apple now allows downloading the last compatible version of some apps (iOS 4.2.1 and later only)
You first have to download the non-compatible version on your computer. Then when you try to purchase the version on your iPod you will be offered a compatible version if one exists.