Trying to find the first job is extremely stressful process. A junior person has no notion of his worth on the market. Each rejection even if only by a lack of any response ("I'm sorry, I'm afraid we are looking for a bit more experienced person" would suffice) can be like a kick on the face when you're just barely learning to walk and most likely is a burned bridge.
I've mentored my girlfriend for 3 years from almost 0 to getting her first job in a company run by a React Native core developer. She had the skill, great attitude, really solid work ethic and very analytical thinking. It'd trust her more with any task than significant number of my past and current senior coworkers. It's hard to prove and no one expects that so naturally her applications had been ignored or rejected. With each one I saw her confidence, self-esteem and enthusiasm crumb. With each positive reply/invitation she was invigorated until the next step came. I'm pretty sure for some the roller-coaster or even worse, being rejected over and over again can be a life defining experience.
Any reply is great, personal is even better. If you spend time describing what was missing from the expectations of your company (don't say "You don't know enough", say "We need someone with more knowledge") and sincerely wish the person well you can be sure they'll be grateful, remember you, work on the gaps and who knows... maybe some day become part of your team.
Please feel free to reach out if you want some example for inspiration.
Edit: Please don't do that against the policy of your company. But if there are no reasons against just ask if you could provide some feedback and resources for the rejection letter.