Martinelli was sent off for shoving Daniel Podence as he took a throw-in and then barging over Chiquinho after Michael Oliver had played the advantage in the same passage of play.
After top-four rivals Manchester United and Tottenham dropped points earlier in the week, the Gunners were able to cling on for the final 20 minutes at Wolves without Martinelli to win 1-0 and move into fifth place in the Premier League.
Under Arteta, the Gunners have had a long-running problem with red cards, but with this being their fourth in six games, the Arsenal manager hinted he will discuss the issue with the Professional Game Match Officials Limited organisation, which oversees Premier League refereeing.
“I’m not happy with the decisions we have had this season, but that is a discussion that I will have with the officials, Arteta said in his post-match press conference.
“To win four matches like that [after a red card] is extremely difficult. We know that and one of the main things we have to stop is that.
Although Arteta was perplexed by Oliver’s decision, he made it clear that his players must avoid similar scenarios in the future.
“I have ran out of ideas,” Arsenal manager Arsene Wenger told BT Sport when asked how he planned to prevent his players from being sent off.
Wolves 0-1 Arsenal: “Gabriel Martinelli was sent off in bizarre circumstances after the Arsenal forward received two yellow cards in five seconds for two separate incidents”