Mikel Arteta has warned Max Dowman that he “is not in Disneyland” and must learn from his red card against Fleetwood after Arsenal’s appeal against his three-match suspension was rejected.

The 16-year-old became the youngest player ever to be sent off in League Cup history on Tuesday as the Premier League champions crashed out to League Two side Fleetwood. Arteta said he was “very disappointed” that the Football Association rejected their appeal against his red card and felt Dowman was lucky not to suffer a broken foot from “reckless tackles”.

But despite describing his reaction as “minimal”, the Arsenal manager revealed he had spoken to Dowman this week to underline his responsibilities after he was also sent off last month playing for England’s Under 19s.

“I’ve done it, so I try to prevent that [in future]. That’s why I’m so protective of these things and especially with young players, because we have made those mistakes. You know how much you can get punished and how much it can change what happens next, and it’s not the first time, so obviously we need to put an end to it very, very quickly,” Arteta said.

Arteta insisted that he had not seen the criticism of his angry reaction to Dowman’s red card when he appeared to aim a few choice words towards the forward as he headed down the tunnel. But he defended his actions after warning Dowman that he was likely to be targeted before the game. “It’s something that we discussed just before we went out, because it’s not the first time that happened,” he said.

“For me, it was the best reaction ever to be able to be who I am. You want to see the reaction of his teammates? When they have to play with 10, you want to see that? That’s the level, and that’s the reaction. But the reaction when I don’t win, you know what the reaction is? I’m pissed off, big time.

“So we need to be ready for that. This is the environment and this is the reality. Otherwise, we are in Disneyland. We are not in Disneyland. We are in the Premier League at this level and we look after him so much that you cannot imagine. But at the same time, we’re going to demand [from] him like anybody else because he needs to earn the right to play.”

Dowman will be suspended for Sunday’s trip to Liverpool and the games against Hull and Newcastle, with Noni Madueke facing a late test to see if he has recovered from an ankle issue that kept him out of the game against Fleetwood. Arteta also revealed that Bukayo Saka is not expected back until at least after the international break as Arsenal await more news on his thigh injury.

Arteta said they had “put every argument on the table” in an attempt to clear Dowman’s name but to no avail. “Very disappointed,” he said. “Especially with the reckless tackles that he received, and then his reaction is minimal in relation to the action.

“I think you have to read the context of the player, the age, and what happened previously. It could have been really bad. And we are lucky today that he hasn’t had a broken foot. That’s clear.”