33 year old Diouf went to Ewood Park on a season long loan from Manchester United and Norwich were left wishing that they had never heard of him as he hit three and could have had more.
Allardyce said after the game: "Diouf scored three very good goals but could have scored more than that - the easiest one he missed when he headed it on to the bar.
"A hat-trick for one of our players is always very encouraging and hopefully he can carry on scoring in the Premier League.
"But he took up lovely positions - for the first goal he drifts off to the far post, gets himself unmarked and waits for the flick-on and then runs in and taps it in.
"His third one he pulls away unmarked at the far post, Morten Gamst Pedersen floats in a lovely ball and he couldn't really miss that one.
"He does look a natural goalscorer in that he drifts into the right positions and that is not coachable.
"If we put balls in those sort of areas he will get on the end of them and that is not what we have got really."