Asked if it was difficult to allow Parker to leave, Allardyce told the Evening Chronicle: "Yes, but at the time we had to let him leave to get Joey Barton in.
"It was a decision I had to take because Joey was top of my list.
"I thought it was the right decision to make based on what had happened to Scott at the back end of the previous season.
"He wasn't too keen when I first spoke to him, but all of a sudden when he went to talk to them, it was on the go.
"If Scott had turned around and said no, that would have been the end of it. He'd still be here now.
"But he was happy with it, we were and we got Joey Barton, so that was fine."