Carrick has stepped into the interim manager role this week after Ole Gunnar Solskjaer's dismissal.
The Englishman played under Ferguson at Old Trafford and can now use his advice in the dugout.
He told MUTV: "It sounds very simple advice, but Sir Alex used to say it quite a bit – well, before almost every game: "Don't be afraid to work hard and express yourself."
"That's something you could take into any walk of life, but it's something that's right, it works, and it's something that we always took on board.
"It's the simplest thing in life: to work hard. Nothing stops you from working hard, whether you're good at it or not. You can still work hard at it, enjoy it and express yourself when you're doing it. If you're doing that then hopefully it's a formula for success."
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