The 20-year-old was asked to take over the role at the beginning of the year after existing Declan actor James Sorensen decided to bow out for a new career in the army.
Speaking about the recast for the first time, Mullally told TV Week: "I was a little shocked, to be honest. When I went to the audition, I wasn't told anything about the role I was going for. It was all top secret.
"So when I found out, there was an initial feeling of, 'I don't know if I can pull this off'. I was completely overwhelmed. What an amazing way to start my career! I'm living the dream of thousands of actors."
Mullally confirmed that he watched "hours and hours" of episodes to research Declan's history before filming his first scenes.
On whether fans will grow to like his version of the character, he commented: "I'm sure that initially people will be quite confronted by a new face with the same character name - I'm not fooling myself about that. But hopefully people will come to accept it."