The Liverpool manager accepts the special feeling around a derby but insists that the Reds will approach it like a ‘normal game'.
City dominated possession from the start against an Everton side that struggled to gain a foothold in the game and created few real chances.
Conte had won all three of his first league tests in charge of Juventus, Chelsea and Inter by an aggregate score of 10-2.
Wolves beat Everton 2-1 in the Premier League fixture at Molineux stadium on Monday.
According to a report by Italian outlet Calciomercato, apart from Arsenal, Real Madrid are also interested in the Everton striker Dominic Calvert-Lewin.
West Ham United goalkeeper Lukasz Fabianski sounded extremely excited after the club's professional all-round performance in a 1-0 win at Goodison Park.
Manchester United could only manage a 1-1 draw against Everton in their last Premier League match before the international break.
Arsenal are reportedly interested in Everton forward Dominic Calvert-Lewin and Aston Villa striker Ollie Watkins as a replacement for Alexandre Lacazette
Anthony Martial fired the Reds ahead just before the break, but Andros Townsend punished Manchester United from a quick counter-attack in the second half.
A second half goal by Andros Townsend denies Manchester United all three points at Old Trafford in the Premier League.