I went shopping, but I realized I forgot to buy eggplants when I got home.
I went grocery shopping and I forgot to buy eggplants but didn't think of it until I got back home.
この場合、次のような言い方ができますよ。
ーI went shopping, but I realized I forgot to buy eggplants when I got home.
「買い物に行ったが、家に帰ってきた時に、ナスを買い忘れたことに気がついた」
ーI went grocery shopping and I forgot to buy eggplants but didn't think of it until I got back home.
「買い物に行ってナスを買い忘れたことに家に帰って来るまで気が付かなかった」
to forget to buy XX で「XXを買い忘れる」
ご参考まで!