Learn Portuguese (Portugal): — Gostaste do concerto? — Nem por isso. - "Did you like the concert?" "Not really."

Literally it translates to "not even for that". It is a highly common idiom used to soften a negative response, much like "not really" or "not particularly" in English.

Why is it do concerto and not just o concerto?

The verb gostar always needs the preposition de before the thing you like. Here, de combines with the masculine article o to make the contraction do.

How do we know this is addressed to the informal "you" (tu)?

The past tense ending -aste on gostaste is exclusively used for tu. Because the verb ending makes the subject completely clear, the pronoun itself is simply left out.

Can I translate "not really" directly as não realmente?

No, translating it literally sounds very unnatural to Portuguese ears. The phrase nem por isso is the standard, native way to express "not really" or "not so much".