Allardyce failed to make his desired striker signing before the tournament kicked off in South Africa.
He told the Lancashire Telegraph: "I am not so sure where we are going to get this key player from because it is a very difficult market in the world of football today.
"It won't be made any easier by the World Cup either because it will only inflate the prices. That is why we went all out in the early months to secure a few players that never materialised.
"Now they have gone elsewhere and we are left still searching to find the player we want. It is very, very difficult indeed to find that player but I am happy with the squad that finished the season.
"Like any manager obviously if I had the time and money to change it in a few areas I would. I would like to bring one key player in and we all know that is a frontman if we can find him.
"Whether we do or not is another matter. But we will have to continue to search the world of football and see if we can find the right player at the right price."