Unai Emery cited concern over Bournemouth's intense approach as the reason he overlooked Mesut Ozil in Arsenal's 2-1 win at the Vitality Stadium.
Pierre-Emerick Aubameyang hit the winner in the 67th minute to extend the visitors' unbeaten run to 17 matches in all competitions.
Playmaker Ozil watched the entire 90 minutes from the bench and was not present as the other substitutes warmed up half-time.
The 30-year-old has not always been an automatic starter under Emery this season and could struggle to win back his place after Arsenal successfully switched to a three-man defence on Sunday.
"We thought about how we can be better in the match," Emery explained in his post-match news conference.
"With a very demanding match physically, with [Bournemouth's] intensity against us, we decided [to leave Ozil out].
"But every player is important. Also, we tried with three centre-backs. It's another opportunity to improve and find our best performance."
The Gunners' next Premier League assignment is a north London derby date with Tottenham at Emirates Stadium.
An Arsenal victory would move them level on 30 points with Spurs, but their head coach is focused solely on the preceding Europa League trip to Ukrainian side Vorskla.
"We are playing Thursday in the Europa League and it's important also," he told Sky Sports.
"At the moment we're first in the group and we want to finish first after the six matches. We are going to think about that.
"Sunday is a very important match, very big match for us and also for the Premier League it's very important. It's the first competition for us.
"We are going to prepare our way, little by little, step by step, think first about Thursday and then Sunday."