Both the midfielders started the Merseyside derby at Goodison Park and played for the entire 90 minutes, as the game ended in a 1-1 draw.
"Liverpool have started to build the pressure, but I have been impressed by Everton's midfield of McCarthy and Barry,” the former Celtic manager said on BBC Radio 5 Live with around five minutes of normal time in the match left.
Former Aston Villa and Manchester City midfielder Barry took one shot, had a pass accuracy of 78%, created two chances, put in two crosses, attempted one dribble, won 100% of his tackles, and made one interception and three blocks.
Republic of Ireland international star McCarthy took one shot, had a pass accuracy of 89%, created one chance, attempted one dribble, won 60% of his tackles, and made one interception, two clearances and three blocks.
Everton are seventh in the Premier League table at the moment with 13 points from eight matches, just two points behind fourth-place Crystal Palace.