Mikel Arteta was "absolutely fuming" with the decision to send off Myles Lewis-Skelly after 10-man Arsenal battled to a 1-0 win away at Wolves.
Lewis-Skelly was shown a straight red card by referee Michael Oliver just before half-time for fouling Matt Doherty 30 yards from Wolves' goal.
Oliver adjudged it was serious foul play from Lewis-Skelly as he caught Doherty on the ankle, though Wolves later had Joao Gomes sent off in the second half.
Arteta was furious with the referee's decision to send off his player, telling Sky Sports: "It is that clear that I leave it to you guys.
"I am absolutely fuming, but I leave it with you. Because it is that obvious. I don't think my words are going to help."
At 18 years and 121 days, Lewis-Skelly is the third-youngest player to be sent off in the Premier League, after Wayne Rooney and Michael Owen.
Asked if Arsenal would appeal the decision, Arteta said: "That's for the club to decide what the best decision is.
"I think it's that obvious, maybe we don't even need to."
Riccardo Calafiori was brought on as part of a half-time reshuffle and fired in what proved to be the winner at Molineux after 74 minutes.
Arsenal have now had more goals scored by defenders this season (eight) than any other side in the Premier League.
Arteta's men saw out the remainder of an ill-tempered game, helped by Gomes being sent off on 70 minutes for a second bookable offence.
In doing so, Arsenal kept their first away clean sheet in 10 Premier League games, ending a run stretching back to September.
"It's incredible what the boys did again," Arteta added. "In the context that we were thrown in again, it was about character.
"It was about the personality of the team, courage and intelligence to play the game we wanted to play. It was exceptional."
Arsenal remain six points behind leaders Liverpool, who beat Ipswich Town 4-1 at Anfield on Saturday and also have a game in hand.
Wolves, meanwhile, have lost their first four league games of a calendar year for just the third time and are outside the relegation zone on goal difference alone.
"It was a tough game," Wolves goalkeeper Jose Sa told Premier League Productions.
"We had a good opportunity to win this game, if we then take our opportunities. In the end, we lose and we are sad about that."