The Gunners got the 2017-18 season underway with a thrilling encounter with Leicester City at the Emirates Stadium on Friday.
Two goals were scored in the first five minutes - one apiece - and ultimately Arsenal came from 3-2 down to win 4-3 with two late strikes.
Wenger told Sky Sports News after the game: "Going forward and character-wise we have been great. We had some avoidable goals which we conceded and overall we have to work on that.
"I don't know how good everyone will be. There are six or seven teams who can win and it makes it interesting. Every point you drop can cost you a lot."
Up next for Arsenal is a trip to Stoke City in the league on Saturday, August 19.