Wales international Davies blossomed during Hodgson's 30 months at Craven Cottage but warned: "Every day is geared towards team shape - and it shows. We would have a little laugh about it now and again, but when he came to Fulham we were fighting relegation. His management style took us to a Europa League final, so you take it.
"I don't want to give any secrets away, but he gets the 11 that he wants for a match and drills everything in that he wants. It's defensive drills and certain attacking drills - with no diagrams. It's all on the pitch with the ball."
Davies, 30, insists Hodgson is the best manager he has ever worked for and his exit could affect his own future at the London club.
And striker Bobby Zamora also paid tribute to Hodgson, saying: "When people were having a go at me, Roy was talking about me for England. He made us hard to beat and when you don't lose you have always got a chance of winning."