The Toffees downed Frank Lampard's men at Goodison Park after Richarlison's opener and a brace from Dominic Calvert-Lewin, with caretaker manager Ferguson seen celebrating each goal wildly along the touchline.
Cole said: "The first tackle that went in, the place erupted and it just galvanised the whole place. Everybody seemed like they had 20/30 percent more.
"You can talk about Duncan and what he can do... that was it - an emotional message, get them together. There wasn't anything tactical today that was special, it was 11 players just together and fighting for the badge. And that was enough for them to get the win today."