YOU SAID:

Today I took a nap, but woke up still tired.

INTO JAPANESE

今日は昼寝をしたが、目が覚めるとまだ疲れていた。

BACK INTO ENGLISH

I took a nap today, but when I woke up I was still tired.

INTO JAPANESE

今日は昼寝をしたけど、目が覚めるとまだ疲れていた。

BACK INTO ENGLISH

I took a nap today, but when I woke up I was still tired.