Laudrup has explained that Graham simply wanted regular playing time and said the club were happy for the deal to go through.
"It wasn't that Danny was unhappy but it was a combination of going elsewhere to play regularly, and especially the chance to go back home, which was his desire," said Laudrup.
"I told him it was okay and I understood, but he had to understand there was the economic side.
"Once the offer from Sunderland was good enough, Swansea as a club were happy and that combination made it clear it was a decision we had to leave him go."
Graham joined the Swans from Watford in 2011.