The Merseyside outfit produced a superb display at the Emirates Stadium, and claimed a deserved point when Gerard Deulofeu cancelled out Mesut Ozil's opener six minutes from time.
Roberto Martinez's side had already chalked up victories over Chelsea and Manchester United this season before their trip to the Premier League leaders, and have lost just once in the top flight this term.
Everton - who are on an eight-match unbeaten run in the Premier League - occupy fifth spot, seven points adrift of Arsenal.
And while Howard stressed the side will stay grounded, he added they are capable of competing with the best teams in the league.
"I think it's the most confident we've been," he told the Liverpool Echo. "We know when we cross the line that we have a formula to win games. It's not guesswork - if we do 'a', 'b', and 'c' we'll get 'd'. That's a good feeling to have.
"We don't want to get carried away because we're not even half way through the season but we're coming into the game and we know how to pick teams apart.
"We've only lost one game and we have a way of playing where we can dictate the game and if that carries on like this we can be successful.
"One of the key things we worked on was doing to Arsenal what they usually do to other teams, and I think that proved a point.
"The stats proved we did it and it says a lot about this team. If we can do all those little things week in, week out we're only going to grow more in confidence."
