The Toffees fancied their chances of ending 22 years of hurt in terms of not winning at Anfield and took the lead after just three minutes when Richarlison struck.
As Liverpool chased the game, Ancelotti brought on Gylfi Sigurdsson and Dominic Calvert-Lewin, and it was the striker that was brought down in the 83rd minute by Trent Alexander-Arnold to hand Everton a spot-kick which was converted by Sigurdsson.
Everton saw out the remainder of the game to claim a famous 2-0 victory and Gray believes it was evidence of just how good a manager Ancelotti is.
“It’s been a sensational day in respect of, we knew we had a great coach, and today he showed it”, Gray said on beIN SPORTS.
“The way he set us up was first class, frustrated Liverpool.
“It didn’t nullify them totally, they created a few opportunities as they are going to at Anfield.
“But in general I thought the way he set the team up was perfect and his use of substitutions later in the game, bringing on a fit Calvert-Lewin to stretch the game, to give them a problem, Sigurdsson to bring a bit of composure, that was just perfect as well.”
Everton have now drawn level on points in the Premier League with Liverpool and sit seventh, just behind the sixth placed Reds, while they also have a game in hand.
Ancelotti is keen for Everton to secure European football for next season.
