United's Yohan Cabaye scored from the free-kick.
Whelan told the club's official website: "It was me who let Newcastle back into the game with my error.
"I can only apologise because up until that, I don't think Newcastle had too many chances, and then I gave them a free-kick in a great spot the boy put it away.
"I can only hold my hands up and apologise and say sorry not only to the lads, but the fans who have travelled up."