The Gunners suffered a shock 2-0 loss at the hands of Bournemouth on Saturday after defender William Saliba was sent off in the first half.
It meant they lost ground at the top of the Premier League and finished the weekend four points behind leaders Liverpool.
But Arteta, speaking at his pre-match press conference on Monday, said there was no need to panic after a first defeat since April.
"You have a defeat, that's part of the game, it happens in very specific conditions as well," he said.
"Let's move on, take that pain we still have in the tummy and use it for tomorrow night."
The Spaniard added: "It puts a bit of perspective into the situation. Obviously, we want to win in any context. The reality is that we have made that context very difficult for ourselves.
"It was very difficult already with the amount of players that we had out and the schedule and the games that we had to play but that's the reality.
"For that game, we didn't get away with it. We could have done and it could have been a very different narrative but the reality is we didn't. Another context is that we have lost one game in six months. Now we have to win again."
Arteta also addressed the issue of red cards, after Saliba became the third Gunners' player to be sent off in eight Premier League games this season, following dismissals for Declan Rice and Leandro Trossard.
"Playing with 10 men, obviously that is an issue," he said. "The truth is when you analyse the three very different actions and the outcome of them, the reasons are very different.
"Regardless of that, we cannot continue to play with 10 men, especially at this level."
He added: "We need to eradicate that, it's clear. Why, the reason and how - it doesn't matter, we have to focus, it has to happen."
Arteta said Bukayo Saka's fitness would be assessed ahead of Tuesday's match at the Emirates after the England winger missed the Bournemouth game.
Arsenal are looking for their second Champions League victory of the group stage against Shakhtar after drawing 0-0 against Atalanta and beating Paris Saint-Germain 2-0.
Arteta said he had "a lot of sympathy" for his Ukrainian opponents, who are forced to play 'home' Champions League games in Germany due to the ongoing war in their own country.
"The things they have to put in place to be able to continue to play football matches at this level and compete in the way they do," he said. "It's remarkable."