Allardyce said: "I think Radhi's impact into the Premiership in the first year was quite outstanding. But I think year two caught up with him and he levelled out. It became a little bit more of a struggle with the pressures of the Premiership, the UEFA Cup and domestic competitions, week in and week out.
"When it's your first season in the Premiership and you've fulfilled your childhood dream, the adrenalin gets you through. But the reality kicks in in the second season.
"That caused me to look in the market and I found what I consider one of the most experienced centre-halves in Europe in Abdoulaye Meite. We went about that task, having tried to sign him two years ago, and we finally got to a figure that suited us and him."
"He is only 25 but is a player with Champions League, UEFA Cup and French league experience and his arrival gave me the opportunity to cash in on Radhi.
"Abdoulaye Faye moving to the back last year showed what a force he could be. With him, Abdoulaye Meite and Tal Ben Haim, I have three very good and very comfortable centre-halves and that has allowed me to let Radhi go and use the money somewhere else."
Meanwhile, 20 year old keeper Chris Howarth has joined Oldham Athletic on a one month loan deal.