Gillan, who joined the show as companion Amy Pond alongside new Doctor Matt Smith, admitted that she was surprised fans liked the changes so much.
"We are all really quite taken aback at how positive it's been, actually," she told DS. "We didn't expect it to go down that well.
"Especially when the first episode came out, it was quite overwhelming actually. So I'm just thrilled. I'm really, really happy."
Gillan added that she is looking forward to filming new episodes of the show, saying: "I can't wait for season six. It's going to be so much fun. And I really miss Matt and I miss the Doctor."
Doctor Who continues on Saturday at 6.40pm on BBC One.