Not too many players are going to significantly improve their hands at 25+ years old. It's not just practice, there is definitely an innate physical ability to do it or not, kinda like hitting a baseball. Tracking the ball is the same way, and he appears to really, really struggle with that based on his punt returns. Of course practice is important but different people are going to have different limitations.
The NFL also obviously plays much faster and the ball is slightly larger than in college, both of which make it tougher to catch.