Arsenal defeat to Bournemouth because they lost in the first leg of the UCL, Arteta had to sacrifice the EPL match to maintain the fitness of the players in the UCL. Literally, the defeat had a big impact on their morale, but on the other hand, they were very motivated to win the second leg of the UCL. Arsenal need just a few more points to secure a place in next season's Champions League, but if they win the trophy they will qualify automatically even if they finish outside the top five.
Aston Villa still maintains their hopes of qualifying for European competition next season, but the last 2 of the last three games are very tough for them, although Man United and Tottenham are not too strong in the EPL this season, but both teams can be a threat to Aston Villa who are hunting for tickets to the UCL or UEL.
I don't think Arsenal was defeated due to the first leg of the Champions League they lost against PSG. If Arsenal didn't want to put effort into the game against Bournemouth, I am confident they weren't going to start with their first XI. I checked Arsenal squad when they were playing against Bournemouth, and I discovered that every player they were going to use in the Champions League started the match, except Timber, who wasn't available in the Premier League game. Arsenal only lost because they did not perform well enough to get a point.
In addition, Aston Villa is in better form right now than they have been since the beginning of the season, I was surprised when they won against Fulham with the odds the bookies gave them, I expected the game to be a draw. Unai Emery wants his team to do everything they can to secure their place in any European tournament next season, but with the next big games, Bournemouth may be difficult to win.