The Gunners decided over the summer that the time was right for change, with the first new managerial appointment made at the club in 22 years.
Wenger was ushered through the exits at the end of an iconic reign, with the Frenchman having been unable to sustain success amid fresh challenges from big-spending rivals.
Emery was drafted in to bring about a reversal in fortune, and the Spaniard believes that he can deliver the consistency required to secure a Champions League spot.
He told reporters ahead of a home date with Everton on Sunday: "The Premier League is very important because I think it is the first competition of importance for us, because that gives us the big credibility on this season.
"Thirty-eight matches give us and give them (opponents) the clarity to show who is the best for the top four.
"It is clear that we have a very, very competitive team to do that - I am confident in my team."
A testing start saw early questions asked of his methods, but Arsenal are now a on four-game winning streak across all competitions.
Positive progress is being made at home and abroad, with the Gunners determined to force their way back among the elite on a domestic stage.
Emery has, however, made it clear that trophies are the top priority for him this season, with the former Sevilla and Paris Saint-Germain boss prepared to sacrifice a top-four finish if he could guarantee another success in the Europa League.
He added: "One choice? For me, the Europa League is very important.
"It is one title and I think for us, every title is the best way, the best performance, the best future."
Emery boasts an impressive history in that competition, with Sevilla having tasted three successive Europa League triumphs under his guidance between 2013-14 and 2015-16.