It was their 10th home win in a row in the league, a run that has included victories over closest rivals Manchester United, Spurs and Chelsea, and puts them in a strong position to seal a top-four spot.
Emery insists it will still be tough to seal a return to Europe's elite club competition, but he is more concerned about establishing a positive rapport with the Emirates crowd than focusing on their league position.
"Our big challenge was to win again and it's not easy to win games consecutively," the Arsenal boss told a news conference. "We showed we can win with different players and formations and the players who came on, their impact was good.
"We want to create that good team spirit. Our target is very difficult and step by step we are getting there. We were lazy after [the first] two games this season, and now we are third, but there are still very difficult games ahead.
"The next challenge away to Everton is a big one as we need to convince people we can also be consistent away.
"We were playing key matches against Manchester United, Tottenham and Chelsea. We had this opportunity and won this opportunity because we were being consistent, winning more matches to be closer to them.
"Now, I know it's going to be difficult [to stay in the top four]. I'm not thinking about that. My first target is to create a big atmosphere. We're creating it little by little."
Aaron Ramsey, who was made captain for the game, scored Arsenal's first goal and was a standout performer until he went off in the second half with what Emery said was cramp.
Emery hopes the midfielder continues to feel happy and committed to ending the season strongly, before he completes his move to Juventus for next season.
"It's clear, there's not more to speak about on that," he said. "The most important thing is he is happy, working to help us and taking a performance to be strong in each match.
"I am happy with him. I want to continue with the same spirit, individually and collectively with all the players. I can only say to him to continue. I hope he will be okay for Sunday [against Everton]."
/ vision— Arsenal FC (@Arsenal) April 1, 2019
@AaronRamsey has now scored against different opponents in the Premier League
@LacazetteAlex has now scored goals at Emirates Stadium in the Premier League alone#ARSNEW pic.twitter.com/1eF6MBrTT3
Newcastle boss Rafael Benitez felt his side were unlucky to be undone by Alexandre Lacazette's late strike, which came following a pass from substitute Pierre-Emerick Aubameyang.
"I'm proud of the players as they are trying very hard," he said. "We were close enough to get something, but they have danger, pace and ability, and players such as Aubameyang on the bench, who is worth 75million.
"I prefer to be where we are and have the points on the table and get three points in the next game. Every game is a final, and we have to be focused and concentrated and see what happens with the other teams.
"Maybe the last match with Fulham will be the one that makes the difference."