The 25-year-old, who began his career with Sunderland, joined Bury in May 2012.
"We feel it was the right thing to do. Of course it was a tough decision," Whittingham told BBC Radio Solent.
"Goalkeepers will always be scrutinised, but if you feel your have to strengthen then you have to do it."
Carson has made 50 appearances for Bury.