Wales manager Gary Speed was found dead at his home near Cheshire on Sunday aged 42.
Big Sam signed Speed while in charge at Bolton.
Allardyce said: “Gary was a great lad and a great pro. To play for as long as he did and as successfully speaks so much about his appetite for the game.
“He wasn’t one of those who thought he knew it all. He was happy to look at new ideas, like sports science, and take them on board. It said so much about him that he always wanted to learn, which obviously helped him in his own management career.
“It’s hard to get your head round it. My thoughts are with his family.”
