The referee, who was in charge of last year's FA Cup final, apologised to the Gunners after the game and will learn later whether he has been dropped for the coming weekend's games as a result of the mistake when the Premier League announces its match officials list later on Monday.
Arsenal are likely to appeal against the dismissal on the grounds of mistaken identity and although the one-match ban will be transferred to Oxlade-Chamberlain, there has been some suggestion the Gunners will then appeal the suspension as the shot appeared to be going wide, and that therefore a goalscoring opportunity was not denied.
Martinez believes referees should be given some leeway in terms of the errors they make and does not believe new rules should be introduced to make greater user of technology.
"I wouldn't think you should put something in place if that happens again because it is so rare and I think at that moment the referee was completely sure," said the Toffees boss.
"I think we would be going a little bit too far. I think goalline technology was a really important breakthrough but from that point on I think we need to allow referees to do their job.
"I am sure in that incident he would have listened to the players and listened to the fourth official to try to get some help, but you need to be strong.
"Andre Marriner has incredible experience and it was one of those situations that happens in football.
"We have an elite group (of referees) in our league and for me it is one of the best in world football.
"We need to increase that group and help them have good training and development but we need to let them get on with their job.
"Errors are part of the game and there will be errors, misjudgments and mistakes but that is part of football and you need to accept it because that is what makes football what it is.
"It should be part of the game. It is not a black and white decision at times, it is a little bit more of interpretation.
"I think we need to rely on the referees and I think the referees in this country are as good as they get."
In Saturday's incident Oxlade-Chamberlain tried to tell Marriner he was the guilty party but the referee stuck to his original decision to send off Gibbs.
Martinez said that was a good rather than bad example of the relationship between players and referees.
"I think there is a really good relationship and referees are the ones to praise in that respect," he added.
"I've seen a lot of leagues around the world and referees don't want to be seen to be talking to the players because they think it means they lose power.
"I think the relationship in the British game is as good as it gets in world football maybe because the referee can trust the players a bit more.
"Abroad the players are there to get decisions from the referee, they are there to try to con the referee so that is not a perfect way to start a relationship."
Former referee Dermot Gallagher believes Marriner should not be stood down this weekend and should be lined up to officiate another game.
"If you are in a position where you're going to stand a referee down for whatever period, whenever he goes back, the focus will be on him," he told Radio 5 Live's Sportsweek programme on Sunday.
"He's made a genuine mistake and that's all it was."
- Sports & Recreation
- Andre Marriner