The Gunners rallied from 2-0 down to claim a crucial three points to restore their five-point league lead ahead of second-placed Manchester City who won 2-0 over Newcastle United.
Thomas Partey and Ben White pulled back goals within eight minutes in the second half, before Reiss Nelson’s 97th minute winner.
“That’s four (wins) in a row - winning four games in a row in the Premier League is very difficult,” Arteta told reporters.
“We’ve won three in a week, which is even harder, and we’ve done it in various ways. That should generate more belief.
“Today, a lot of things went against the team. Our fault for the first one, then the fact we werent scoring, the situation with Leo, the set-play they had when they scored.
“The team still found a way to win the game and thats really positive.”
Leandro Trossard limped off in the 22nd minute with an apparent injury which the Spaniard conceded was a concern.
“It is a worry,” he said. “He came to me straight away and told me he could not continue because he’d felt something when he was tracking back after the corner. We have to assess him and see how he is.”
Arsenal conceded inside the first minute, with Philip Billing putting the Cherries ahead inside 10 seconds, which Arteta labelled “poor”.
“Credit to them. They try many different things from kick-off, they have routines for every single set-play,” he said.
“I’m sure they worked on it and today they scored a really good goal. It was really poor from us.”