The show's executive producer said that the pair are "exactly right" for their respective roles as the Eleventh Doctor and his assistant Amy Pond.
Recalling the moment Gillan was cast as Amy, Moffat told Doctor Who Magazine that all of the actresses who auditioned for the role were good.
"All credit to [casting director] Andy Pryor, everyone we saw for the role of Amy was terrific. Genuinely, every single one of them. There wasn't a single bad audition, they were all brilliant.
"Karen was the very last person we saw and she just fitted better. She was just exactly right. And exactly right with Matt, in that she's a bit kookier, I suppose. A bit madder."
Moffat also revealed that Smith was present at all the auditions for the role of Amy.
"This was his first experience of seeing what it's like when somebody just completely nails the part," he said. "To this day, I still don't know how Karen didn't know she had got the part. She didn't have a clue."
He added: "We were all making faces at each other and waving cos she was just so good, so brilliant!"
Gillan has previously admitted that she was "intimidated" when she was first introduced to Smith, claiming "it was all very scary".