The tennis star and his wife Mirka welcomed twin daughters Myla Rose and Charlene Riva in Switzerland on July 23.
Speaking to People, he said: "Thank God nobody is judging me on it! It's hard, but I'm still trying to be good at it.
"It's been a lot of fun being a father and spending time with them. I'm hands on as much as I can because every day something is new and something different. I don't want to miss anything."
The 28-year-old added: "It's an amazing feeling to be called a dad. I take a lot of pride in that title."
Federer recently opened up about why he never revealed that his wife was expecting twins until they were born, explaining that he was just following doctors' orders.