少し酔いが回ってしまったようですね。すみません、意味の分からないことを言って・・・。

。、・・・。

The alcohol seems to have gone to my head a bit. Sorry for saying things that don't make sense...

Literal

A-little intoxication [subject-が] circulated-[regret-てしまった][seems-ようですね]. Sorry, meaning [possessive-の] not-understood things [object-を] saying...

酔いが回る 'the alcohol goes to one's head, to become intoxicated' — 酔い 'intoxication' + 回る 'to circulate.' てしまったようですね shows rueful self-awareness. 意味の分からないことを言って 'saying incomprehensible things' — a self-deprecating apology mid-drink.