The Gunners began the 2024-25 campaign with consecutive victories, and looked well set to maintain their 100% record in Saturday's lunchtime kickoff against Brighton.
Forward Kai Havertz lobbed the onrushing Bart Verbruggen to open the scoring and give his side a slender half-time lead.
However, the complexion of the contest changed when Rice was shown the first red card of his career in the 49th minute.
Rice was booked for a wild challenge in the closing stages of the second half but there was some controversy surrounding the decision to give him a second yellow.
Arteta criticises lack of consistency
Referee Chris Kavanagh ruled that Rice had delayed the restart by poking the ball away after initially being penalised for a foul on Joel Veltman, who escaped punishment for swinging a leg into the England international.
Arteta criticised a lack of consistency in officiating, suggesting that Brighton were not punished for similar offences, including a moment where Joao Pedro blasted the ball away after it went out of play.
The Arsenal boss told reporters: "I was amazed. Amazed, amazed, amazed because of how inconsistent decisions can be.
"In the first half, there are two incidents and nothing happens. Then, in a non-critical area, the ball hits Declan (on the back of his leg), he turns around, doesn't see the player coming and touches the ball.
"By law, he [the referee] can make that call, but then by law, he needs to make the next call, which is the red card so we play 10vs10. This is what amazed me. At this level it's amazing."
Rice to miss North London derby
Not only did the red card change the momentum in Saturday's contest, but it will have an influence on the North London derby after the international break.
Rice will miss the much-anticipated match due to suspension, leaving Arteta to consider alternative options for his midfield.
Summer signing Mikel Merino would be the obvious candidate to replace Rice, but Arteta has already confirmed that he will be out for a "few weeks" after sustaining a shoulder injury in training.
With Merino likely to miss out, Arteta could turn to Jorginho to operate in midfield alongside Martin Odegaard and Thomas Partey.