Arsenal eventually ran out 3-1 winners in Athens to take a commanding lead back to Emirates Stadium, but they were made to work for it.
Martin Odegaard opened the scoring in the 34th minute, but Arsenal let Olympiacos back into the match when Bernd Leno played the ball out to Dani Ceballos – who was dispossessed and punished as Youssef El-Arabi slotted the equaliser.
The goal was the 14th Arsenal have conceded in 2021 and the seventh to come about as a result of their own errors.
The Gunners eventually won the game thanks to late goals by Gabriel Magalhaes and Mohamed Elneny.
But asked what he would say to people who claim Arsenal are their own worst enemy at times, Arteta replied: “They are not far off.
“The goals that we have conceded, or the chances that we have conceded, they are coming from ourselves.
“That’s really positive because the moment we stop it obviously we are going to be even stronger.
“But the reality is we have to stop it immediately because if not the games are all the time there to drop points.
“But it is my responsibility, I make them play the way we want to play.
“It is just understanding the risk and rewards, when they are, the balls that we have to play and, as I say before, when [we play the balls].
“We have to get better at that, because if not it creates tension, insecurity and it creates belief in the opponent – and it is unnecessary.”