Allardyce, speaking to Zoo magazine, said: "Rafa would be very lucky to be in a job if he hadn't got to two Champions League finals, because they have had some very, very poor finishes in the Premier League.
"While they are a very good Champions League team, they are not a Premier League-winning team yet.
"They don't have that mentality to win that yet.
"Being a foreigner, Rafa doesn't understand it's supposed to be Premier League first and Champions League second."