The Gunners have made considerable progress under the Spanish coach in recent seasons but haven't won silverware since lifting the FA Cup in 2020 and the club legend is disappointed by their lack of major honours.
Speaking on the 'Stick to Football' podcast, Henry said: "I'm not saying that I'm disappointed with Arsenal, but it's normal that people are raising questions now about what the team is doing.
"I understand that at the very beginning you arrive and it's not your team. You need at the very least three or four transfer windows to change everything that you want to.
"It takes time and you have to give a manager time to be able to implement what he wants to do.
"For the last three years Arsenal have been in a situation where they should have at least brought one cup or [reached] a final."
Henry compared his former team to Manchester United - who have played in five finals in as many years despite struggling in the Premier League.
He said: "Manchester United have played in five finals in the last five years, the United that everyone laughs at - whereas for Arsenal in the last three years of building, they've not reached a final.
"So I do understand when people ask the question: 'Surely you should compete for a trophy?'"
Arsenal suffered from their lack of a centre forward this season and Henry questioned why Arteta did not address his team's flaw in the transfer market.
The former France international said: "When you look at the injuries and you look at the players that came, OK, he brought players – he got [Raheem] Sterling when everyone wanted a nine. He had time to get a nine, he had time.
"I’m not the coach, I don’t know how the discussion… everyone has been screaming for a nine – apart from when we win, by the way. When we beat Real Madrid, we didn’t need a nine. No, you do need a nine."