Darcey indicated that Sky entered initial talks with Virgin Media about a carriage deal for Sky Atlantic, but the two firms were some way off agreeing a price.
He said that Virgin Media would "love Sky Atlantic and love it on the cheap", but Sky offered the channel at a price it believes was "very reasonable".
Sky Atlantic launched on Tuesday with acclaimed American dramas Boardwalk Empire and Blue Bloods. The channel will also become the new UK home for all HBO programming.
Speaking at a Broadcasting Press Guild event, Darcey said that he does not want to see Virgin Media secure Sky Atlantic for a low price, as that would mean Sky subscribers having to "cross-subsidise Virgin Media customers".
He added: "Negotiating with Virgin Media is too strong a word. The team went down... and made quite a substantial pitch [and] explained what we thought was a fair price. Thus far they have not been persuaded."
Darcey said that Virgin Media's "enthusiasm" for content had always been "a little bit lukewarm", presumably referring to the sale of Virgin's Living TV Group to Sky last year.
Also at the event, Darcey said that Andy Gray and Richard Keys "crossed the line" with the sexist behaviour that led to the two presenters leaving Sky Sports.
"I think that [Sky Sports managing director] Barney Francis and every other broadcaster in the light of the national debate will ask a range of questions and check they are happy where they are," Darcey said.
"There has been a lot of debate - can you get in trouble for personal opinions, personally held, or when talking with friends down the pub or off camera?
"In the end I don't think that is why Andy Gray left. What happened was that we have a pretty clear view at Sky of the sort of culture we want and the way employees are expected to treat each other. When behaviour crosses that line it is unacceptable."