Smith revealed he had received a "good luck" text message from Piper on Thursday shortly before the premiere.
He also described his co-star Karen Gillan as the "sexiest companion that ever lived".
'Gangling and shambling'
Gillan spends most of the episode in a policewoman's uniform with a short skirt.
She said: "What I love about Amy is that she has this feisty, independent, strong-minded exterior but underneath it all we know that she's actually this lost soul inside because of the way she meets the Doctor."
Both Smith and Gillan said they had already had a positive reaction from fans. "We've had lots of lovely letters," the actress said.
Smith added: "There's one fan who compares me to a hedgehog a lot, which is puzzling, but I've not had any bizarre requests. Everyone's been very kind and generous."
William Hartnell - 1963-66
Patrick Troughton - 1966-69
Jon Pertwee - 1970-74
Tom Baker - 1974-81
Peter Davison - 1981-84
Colin Baker - 1984-86
Sylvester McCoy - 1987-96
Paul McGann - 1996
Christopher Eccleston - 2005
David Tennant - 2005-10
Matt Smith - 2010-
As well as a new Doctor and companion, the episode also unveils a new-look Tardis interior.
The new console looks like it has been constructed from items out of a junk shop, including an old typewriter, a telephone, pressure gauges and a Morse code machine.
Smith has taken over the lead role from David Tennant, who played the time travelling hero for four years.
The new series is also overseen by a new creative team, led by experienced TV writer Steven Moffat, as Russell T Davies has also stood down as the show's producer and chief writer.
Moffat said Smith's Doctor was very different from his predecessor.
"David was sort of neat and fastidious like a humming bird. Matt is gangling and shambling - he's like a terrible mess that somehow becomes elegant by magic, he said.
"He brings back genuine madness to the role of the Doctor - Matt's Doctor is bonkers."
Filming on the 2010 series is still under way - and due to end on Saturday.
Doctor Who began in 1963, and seven actors played the Doctor before the show was dropped in 1989.
After a TV movie in 1996 - starring Paul McGann - the TV series returned in 2005 with Christopher Eccleston in the lead role. Tennant took over in the same year.
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