Alas, no matter how you look at it, it's still my fault.
Tips
usage
嗳 (ài, 4th tone) expresses regret or lament. Note: the same character 嗳 read as ǎi (3rd tone) means to belch (打嗳气). Context and tone mark are essential to distinguish them.
The mouth radical on the left marks 嗳 as a vocal exclamation - a sigh of regret, surprise, or mild dismay. Spoken-emotion particles almost always carry 口: 啊 ah, 哎 alas, 唉 sigh, 噢 oh. 嗳 sits squarely in this family of breath-out interjections.
爱 supplies the sound ài unchanged - purely as a phonetic syllable. The semantic of love doesn't carry into 嗳; this is just the spoken sigh "ai" written with the most recognisable ài-syllable as its tag. The same trick of borrowing 爱 for sound shows up in dialectal 嗳哟.
