Savage told The Sun: "Martin is the boss - there's no two ways about it.
"It's either his way or the highway.
"It doesn't matter how big a name you are, Martin will treat you exactly the same way as anyone else. I don't know what it is about him - it's impossible to describe. He has this fearsome aura, almost like a boxer going into a ring.
"If it's possible to put it this way, I suffered a nice fear. It was excitement, fear and an adrenalin rush all rolled up in one.
"If you went out there and did it for him you went home feeling like the best player in the world. That's the effect this man has on you.
"He had difficult characters at Leicester - guys like me! I responded to him and so did characters like Stan Collymore, whose career was at its lowest point when he arrived.
"He has this incredible aura that just makes you want to play for him."
Welshman Savage added: "He is a brilliant man-motivator and he takes absolutely no messing - as I found after a game against Sunderland when Stefan Schwarz rolled over and over after one of my tackles.
"I knew it was a fair challenge but he was doing all that stuff and I stood over him telling him to get up. After the game a furious Martin O'Neill got me and said: 'Ever do that again and you will never play for this club again'.
"Like I said, you do it his way - or not at all."