The tennis champion surprised fans last month when he announced that Mirka had given birth to identical twin girls Myla Rose and Charlene Riva.
Speaking to The New York Times, he said that he was informed by doctors not to disclose the news and "the next thing you know, I'm seven months through the year and at the end, nobody's really asking me questions about if it's twins or not.
"And then I said, 'Alright, I'll just play along until the very, very end'. I had to really battle myself. I had a couple [of interviews] where I said, 'We're really excited to have some babies', and I was thinking, 'Is that already giving it away?'"
The player went on to say that he could tell his newborn daughters apart "very easily now" because they had different weights and colourings.
He added that he had spent three weeks sleeping at the hospital after the twins were born and that he had received a congratulatory message from long-time rival Rafael Nadal.