Defender William Saliba was shown a red card on the half-hour mark after pulling down Bournemouth striker Evanilson and preventing a goal-scoring opportunity.
While Arsenal weathered the storm of previous sendings-off to grab draws against Brighton & Hove Albion and Manchester City, this time they came up short.
"After 30 minutes, you get down to 10 men, you have to play 67, 68 minutes in this league again with 10 men - that's an accident waiting to happen," Arteta told Sky Sports.
"It's a game of errors - for me tonight, we made two big ones that have cost us a game. And yeah, it's the third time we play in games with 10 men, and at this level, it's very complicated."
After a bright start for the visitors, Bournemouth made the most of their advantage, dominating for long spells and conceding very few chances as a Ryan Christie goal and a Justin Kluivert penalty sealed the win.
Arteta gave credit to the hosts for their victory, but felt that his side had to bear their fair share of the blame for the errors they made.
"They (mistakes) are part of football and it's not the moment to point the finger at anybody, because (the players') attitude is excellent, and they really want (to win), and they really try," the Spanish coach explained.
"It's been tough mentally as well, to play for those long periods in this league, in these conditions, but today unfortunately we paid the price."