Alexandre Lacazette earned the Gunners a point at the Emirates Stadium on Saturday, cancelling out James Milner's second-half opener to extend the north London outfit’s unbeaten streak to 14 games.
Emery, who succeeded long-term Gunners manager Arsene Wenger in May, has not lost a game since the defeat against Maurizio Sarri’s Blues, and felt his side's performance against Liverpool highlighted the progress they have made in recent months.
“The Premier League is the first competition for us. It gives us the big regularity for the season – 38 matches,” the 47-year-old told reporters in his post-match press conference.
“It's very important when you play against City, Chelsea and Liverpool and if you win it's better.
“Maybe after Manchester City and Chelsea, today we are more near those teams, but we need this quality in every match. Every game is important.”
Emery was also keen to praise youngster Alex Iwobi for his contributions, highlighting the 22-year-old’s ability and encouraging his continued growth.
“[He] can impact hard in the match,” the coach added. “First he started on the right, then I thought he was better left. His impact in some moments in the match, like our goal, is important.
“His energy is important, so is his quality. He can improve. He can do better. He scored against Chelsea, I want him to be nearer the box, having chances to score more.
“He can. He is very young. He is improving. But also he has the ambition to do more.”
Arsenal are now fifth in the Premier League table, four points behind leaders Liverpool.