The former Coronation Street star, 53, received the accolade for services to drama from the Duke of Cambridge at Buckingham Palace on Tuesday.
Lancashire, whose three children watched her receive her award, said she had been nervous because "I don't do things like this very easily".
She said: "I think it is an emotional moment.
"I wish my father had been alive. I think at times like this, really, one tends to focus on parents and my father would have been the proudest man in the world."
She added: "It's very difficult because you are in these most spectacular surroundings and you are trying desperately to take it all in but your head is full of white nose because you don't want to fall over when you courtesy.
The Oldham-raised Bafta-winning actress has enjoyed a career spanning four decades.
She has starred in popular television programmes, such as Corrie, where she played Raquel Wolstenholme from 1991 to 1996.
More recently she has gained critical acclaim in roles in drama series, including comedy-drama Last Tango in Halifax and crime drama Happy Valley.
She said she hoped to produce more of both shows, which were both written by Sally Wainwright.
Lancashire added: "She has intentions to return to both Tango and Happy Valley.
"Happy Valley is unfinished business so we have to go back and finish that off.
"And Tango is always a delight... we have sort of become a family away from the screen as well so it's a lovely piece to work on."
One of her next on-screen projects will be the 'dark' Channel 4 drama Kiri in the new year.