Jisho

An adverb modifies a predicate (so a verb or adjective phrase in Japanese), while adjectives modify noun phrases (nouns or pronouns, basically). Now, 大した is a pre-noun only adjectival, it cannot be used as a predicate (also, adjectivals need an auxiliary である to form predicates, but I digress), it can only be used to "describe" a noun, so it can only come before a noun, hence its name. In case this linguistic gibebrish is not making too much sense to you, here are some examples:

２人の人間の経験は、誰だって大いに違います。
The experience of two people differs greatly/is widely different, no matter who they are.

床に牛乳をこぼしたのはそんなに大したことじゃないよ。
It's not that big a deal that you spilled milk over the floor.

Hope this helps.