The Magpies secured a late 2-1 victory following their equaliser, which Whelan gave away by gifting Newcastle with a free kick on the edge of the penalty area.
"It's frustrating for us all, but even more so for me because it was my fault that Newcastle were allowed to get back in the game," Whelan told the club's official website.
"It was my error, and I can only apologise because up until that point they hadn't really caused us too many problems. I hold my hands up for it, and have apologised to the lads.
"Obviously I want to apologise to all the supporters too, especially those who travelled all the way up here. It's a hard one to take, especially for myself."
The Potters are 11th in the Premier League table with nine games left to play.