The French striker missed a gilt-edged close-range header while he also had a goal disallowed by the video assistant referee due to Granit Xhaka being offside and interfering with Leicester keeper Kasper Schmeichel after Lacazette glanced on a corner.
Lacazette has netted three goals this season but none in their past five matches in all competitions.
“Obviously, strikers need goals and he started tonight, he looked sharp and he was really aggressive in his play,” Arteta said.
“Yeah, he had an opportunity to score that goal and he didn’t. I just support them and give them more confidence and try to create more.”
The Spaniard was also disappointed that Lacazette’s goal was denied by the VAR, admitting the decision was harsh.
“Yes because Granit is behind Schmeichel, he is not in front of him so he is nothing to do with that ball, it is away from him and Granit is behind,” Arteta said when asked if he felt the decision was harsh.
“But it’s okay, they made that decision and we cannot change it.”
Meanwhile, Leicester boss Brendan Rodgers was thrilled that his plan paid off as the Foxes claimed their first win away to Arsenal in 47 years, with substitute Jamie Vardy coming on to score the 80th minute winner.
“I don’t know about masterplan, but it was the plan,” Rodgers said.
“It was the idea to deny space and keep our lines tight, and then obviously play through the pressure, so yes, it worked very well for us.
“I thought we started the game well, first five or 10 minutes. We had good possession and then, of course, when you come away to play against any top team, you’re going to have to deal with pressure.”
Elsewhere on Sunday, Everton’s strong start to the season was halted with a 2-0 loss at Southampton, while Newcastle leveled late to claim a 1-1 draw at Wolverhampton.