Having treaded water during the twilight of Arsene Wenger's 22-year tenure in charge, Arsenal have played with a fresh dynamism and charisma, which they displayed as they climed a credible draw with Liverpool at the start of November.
Barely six months into his role at the Emirates Stadium, Emery has lofty ambitions and feels his side should look to Liverpool's recent success under Jurgen Klopp as evidence they can breach the gap.
"Liverpool were without the Champions League, they had the Premier league and Europa League.
"Two years later, they were playing in the final of the Champions League.
"That's a good example for us - maybe we cannot do the same, because it's very very difficult and they worked very well with [Jurgen] Klopp in this progression.
"But my idea is the difference between us and other teams now - Manchester City, Chelsea, Liverpool - we can reach the same level of performance as them.
"But we need time, we need work. In football the test is the next match."
Though Arsenal have shown significant improvement since the back-end of Wenger's spell, Emery feels there is plenty of room for improvement.
The main area in need of development is in defence where Arsenal have shipped 15 goals in 12 Premier League games, and have kept just two clean sheets.
Emery has said Arsenal "lost defensive structure" prior to his arrival and he is demanding a raise in standards.
"Today I was speaking in the dressing room with the players for half an hour, different things, tactically and other things," the ex-Paris Saint-Germain boss stated.
"We have scored 26 goals in the Premier League. That's very good for us. But how many have we conceded? 15. That is a lot.
"At the moment the balance is positive, but it is not enough.
"We need to keep the scoring statistic, but concede fewer chances and let in less goals.
"Sixteen games without losing, that's fantastic. But the last three we have drawn. That is not enough at the moment."