Arteta spoke to Sky Sports after Kai Havertz's header and a string of saves from David Raya sealed three points against a Burnley side who caused Arsenal genuine problems despite their relegation.
"We knew it would be tough because of what it means. We're happy but now I start to worry. We didn't concede anything but ten in the Premier League — you never know. It's another massive one. It's one of the best football we've played this season. We could have had two or three goals."
He was asked about the challenge Burnley posed, praising their organisation under interim head coach Mike Jackson.
"It's never going to be easy. They are a top team, they are really well coached and every team has an incredible spirit."
Arteta said he had not seen the Havertz challenge that sparked debate over whether VAR should have recommended a red card, distancing himself from any controversy.
"I haven't seen it. I was there with our people and I haven't had a chance to look at it."
On the prospect of Arsenal watching Manchester City's Tuesday night game against Bournemouth together, Arteta was non-committal.
"I don't know yet. We have to prepare them for Crystal Palace in the best possible way."
He was equally measured when asked about the reported likelihood of Pep Guardiola leaving City.
"Once he makes that decision, then we can talk about it."
Arsenal will be confirmed as champions if City fail to beat Bournemouth on Tuesday evening, or if they win at Crystal Palace on Sunday.