The Gunners lost their fourth league match of the season against the Cherries, failing to extend their nine-point lead at the top of the table to from Manchester City, who have two games in hand.
Swede international Vikor Gyokeres scored the equalizer for the home side and admits the North London side's performance was not up to par.
"We didn't come up to our level throughout the game," said the centre-forward after the match.
"I think when we scored to make it 1-1, we felt good as a team. We had some dangerous chances before that, and we wanted to take control of the second half, but maybe we didn't create enough in attack.
"They didn't create so much either, but they were clinical and they scored on the chances they got. That's why it wasn't a good result today."
Gyokeres has now scored 18 goals in all competitions since joining Arsenal from Sporting Lisbon, whom they face in the second leg UEFA Champions League quarter-final on Wednesday with a 1-0 lead on aggregate.
"We have a lot of important games to come, and we need to embrace it and to enjoy playing those games," added the 27-year-old.
"Like I said, it's a great game to have in a few days, so we just need to recover now, leave this behind and make a very good performance on Wednesday."
Liverpool teenager Rio Ngumoha has expressed his gratitude for coach Arne Slot's belief in him after his brilliant opener in the 2-0 win over Fulham at Anfield on Saturday.
Liverpool brought a disappointing run of results to an end with a 2-0 victory over Fulham at Anfield, keeping themselves in the Champions League qualification spots.
Arsenal's push for the Premier League title suffered a damaging setback as they fell to a 2-1 defeat against Bournemouth at the Emirates Stadium, ending their nine-match unbeaten run in the league.
New Tottenham Hostpur head coach Roberto De Zerbi insists he would like his team to emulate the football they played under Ange Postecoglou as they look to avoid relegation from the Premier League.
