A double from Martin Odegaard and a strike by William Saliba fired Arsenal to a 3-0 win over promoted Bournemouth on Saturday, the first time since 2004 they have opened the season with three successive victories.
Arteta was delighted with the start but added that top spot in the table counted for little this early in the season.
"It's just three games, it doesn't mean anything," the Spaniard told reporters.
"What it means is the team is playing really well, we won three games, we're scoring goals, we're keeping clean sheets, the team is playing and performing well, it's competing really well."
Arsenal signed striker Gabriel Jesus and left back Oleksandr Zinchenko in the transfer window and both have impressed, while defender Saliba has also shone following his return from a loan spell at French side Olympique de Marseille.
Arteta said they were still in the market for new players despite the squad's strong showing in the opening weeks.
"We don't like reacting obviously, we want to get the players that we believe will make a big impact in the team. If we can do that, we will try to do that," he said.
"We know as well where we are short, where we have to add more firepower. And if we can do it, we will do it."