I've taken naps and rests here and there after my workouts all my life. It's called listening to your body and giving it what it needs. There's a tradition among 14ner baggers (people who hike the 14,000' mountains in Colorado) of taking a nap on the summit. When you get to the top, it's not uncommon to see a lot of "dead bodies" lying around, their packs off, their sunglasses on, and the remains of their lunch strewn at their feet. It's kinda fun waking up from a deep, short sleep on a rocky peak in the middle of nowhere, looking around and asking yourself, "How the hell did I get up HERE?"
If all you need to get your energy back after a killer lifting session is a short snooze, consider yourself lucky. If you are still tired after your nap, then yeah, it's a nutrition thing and you would do well to make some adjustments. My personal routine is to lift, munch protein, snooze, wake up, eat some fruit, and then dive into the next phase of the day. By the by, naps can be ten minutes or an hour, don't let anyone tell you that twenty minutes is the only legal "nap." Let your body take what it needs and learn from that. It will be different each day.