"Fully agree, I value more this victory than any other this season," Arteta told reporters.
"Coming from playing every three days (they beat Atletico Madrid in the Champions League on Tuesday and next play Brighton in the League Cup on Wednesday), you play against one of the teams I think is one of the best, when you lose that concentration they can punish you.
"A massive win. We knew the difficulty of it."
The victory, sealed by a stunning set-piece goal from Eberechi Eze against his former club, widened Arsenal's lead at the top of the league table to four points. But Arteta was quick to temper any title talk.
"It's very early, we're still in October," he said. "The emotional state is really high but there are a lot of things to get better. Let's try and recover for Wednesday."
Rivals Manchester City and Liverpool both lost this weekend, which contributed to Arsenal's gap.
"It shows you how hard this league is," Arteta said. "The players aren't allowed their phones so I hope (that they weren't following other results).
"We are where we are," he added. "It's a credit to us because we have been very consistent. It doesn't mean much other than we are doing a lot of things."
The match-winner came from a set-piece, an area Arsenal have clearly refined. They have a league-high 11 goals from dead-ball situations.
"We have noticed a shift, methods that are implemented that are more efficient," Arteta said. "You can contain the spaces, because you are better and we have to find a way to score in different ways."
Eze's brilliant finish that obviously held a lot of meaning coming against the team for which he played for five seasons drew praise from his manager.
"He was super relaxed before the game," Arteta said. "Such a strong feeling and gratitude. The technique (on the goal) is unbelievable. We needed something (special) against a team so well organised."