Doubles from Alexandre Lacazette and Pierre-Emerick Aubameyang, along with a stunning goal from Aaron Ramsey, saw the Gunners cruise to a ninth successive win in all competitions on Sunday.
Their victory moved them into the top four, but Emery insisted that his team must continue to prove their winning mentality in the coming fixtures.
"When we are winning now, I think we need to be in the same way in our mentality. We are going up in the table little by little, giving us a better position for our objective.
"I am just thinking about the next match at the Emirates, with our supporters. I want to show them we are improving with our quality, with our mentality and, above all, with the commitment we had here.
"We are happy. We need to feel together, inside with the club and with the players.
"[We need to] be calm, enjoy working, stay together, but improve individually and collectively and find our best performance in each match with combinations from the players.
"Because we need to continue to improve and we can."
Lucas Torreira has quickly become a key figure in Arsenal's midfield under their new manager, and Emery singled out the former Sampdoria playmaker for individual praise.
"He is very young. This is his first experience at this level but he was playing in Italy and with his national team," Emery said.
"Here, he is doing very well. The first impressive thing is his humility every day. He wants to listen, to learn.
"He played in the middle, on the right and his performance is the same. His career is starting and we want him to give us his best performance and his quality."
Arsenal return to action after the international break in just over a fortnight when they host Leicester City on October 22.