The 22-year-old completed a reported £15m switch from Swansea on Friday, with the Team GB star signing a long-term deal at Anfield.
Allen, who had a higher pass completion percentage than Barcelona’s Andrés Iniesta last season, helped the newly-promoted side to a respectable 11th-place finish in their first season in the Premier League.
“This boy, when you see him play you’d think he was Spanish, a real European player. I would have paid many more millions for this kid,” said Rodgers.
“He’s unique in that he is a British player who just does not give the ball away. You will see the difference he can make.
“He’s incredible on the ball, his body work is very intelligent, for a 22-year-old it’s frightening.
“Joe’s game understanding is very, very good and he is in love with the football, he loves it, he wants it all the time.
“He has so much courage to get on the ball and play and I think he will fit in really, really well with all the other players.”
Rodgers is confident Allen will slot seamlessly into his Liverpool side as the 39-year-old attempts to imprint his footballing philosophy on the 18-time English champions.
“Joe is a player whose profile will fit perfectly with the ideas of this group,” Rodgers added.
“His ability to control and dominate the ball is an important ingredient in our attempt to gain success on the field.
“Joe has had a fantastic education at Swansea City and will now begin the next chapter in his exciting career, and I wish him all the very best in what I’m sure will be a long and distinguished career here at Liverpool.”
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