Saliba had been initially booked for the foul but the decision was overturned after referee Rob Jones was recommended to do an on field review.
Arsenal went on to suffer a 2-0 defeat at the Vitality Stadium, with Ryan Christie and Justin Kluivert securing a famous win for Bournemouth
Saliba is now set to miss Sunday's showdown with Liverpool and Arteta says the Gunners are yet to decide whether they will lodge an appeal.
Mikel Arteta has provided an update on whether Arsenal will appeal William Saliba's red card
'I leave that more to the club to understand the circumstances. They will have to decide it,' the Spaniard said ahead of his side's Champions League clash with Shakhtar Donetsk on Tuesday.
'It is about perspective. We want to win in any context but the reality is we made it very difficult for ourselves.
'Another context is that we have lost one game in six months. Playing with 10 men there is obviously an issue. When you analyse the three different actions and the outcomes it's very different. We cannot continue to play with 10 men.
'The task becomes almost impossible. We need to eradicate that. I think what happened in those three cases is nothing to do with aggression in my opinion. We want to competitive. It's great.'
Saliba's red at the Vitality Stadium means Arsenal have gone down to 10-men three times in their opening eight matches of the season.
The Gunners' first sending off of the season came at home to Brighton when Declan Rice was given his marching order for a second bookable offence after delaying a restart.
Mikel Arteta's men had led 1-0 thanks to Kai Havertz but the match ended in a 1-1 draw as Joao Pedro earned the Seagulls a point.
Arsenal also went down to 10 men when Leandro Trossard was controversially sent off for a similar offence away to Manchester City, with the match ending in a 2-2 draw thanks to a last-ditch John Stones strike.