Marcus Rashford scored twice in the second half as United, who beat Liverpool at the start of their four-game winning streak in the Premier League, punished the visitors on the break.
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But while there is a renewed sense of belief around the club, the Dutchman was quick to dampen talk of United being close to competing at the very top of the table.
"I understand fans are dreaming and the standards of Manchester United have to be good, but we’re at the start of a process, we’re still far away," the former Ajax manager told reporters.
"We have to get doing things much better than we do, that’s an investment -- we have to do that way together every day, bring those high standards to Carrington (training ground. We have to get better if you want to win trophies in the end," he added.
Ten Hag was pleased, however, to see that a United team that had been so fragile last season did not panic when Bukayo Saka brought Arsenal level on the hour.
"The spirit from this team, they can deal with setbacks, it is really great and shows the mentality - we have really improved on that," he said.
"We have the right characters and now it is about cooperation, deal with set backs but also improve - we have to stay calm, stay composed and play our game," he added.
What was not yet evident in United's play, beyond the early exchanges, was a sustained control of the game as they were limited largely to counter-attacks.
Ten Hag said he wanted to see more of the kind of intense pressure they produced early in the match.
"I thought the first 10 minutes was the best we have played so far this season. But after the cancelled goal it wasn't as good," he said.
"We had a good plan, we didn't get it all on the pitch, we couldn't control it when we should have. We got a set back and we fought back, that's good to see. I like this mentality."
