The Gunners boss would rather be in the Champions League, with time to catch Mancini's men in the league, than be knocked out of the CL this early in the season.
Arsenal manager Arsene Wenger has insisted he would never "swap places" with Manchester City, despite trailing the Premier League champion by 12 points already this season.
Wenger, whose side confirmed top spot in its Champions League group with a game to spare, insisted he would rather still be in competition with over 20 games left of the Premier League campaign to catch the champions, than be eliminated this early in the season.
"I wouldn't swap places with Manchester City," Wenger told reporters. "We have 23 games to come back on them in the league, but in the Champions League you're in or out."
The 63-year-old has also admitted that the players were very unhappy following their 2-0 home defeat against Swansea, however he dismissed reports that assistant manager Steven Bould gave the squad an angry dressing down after the game.
"Nothing really happened after the [Swansea] game," he added. "But the players were not happy. You want them to dance? This group of players is highly motivated and if they don't win, they are upset.
"I'm more worried if I see players in the shower who laugh after they have lost. The most important thing is to win the next game and show how good you are."
Wojciech Szczesny is looking forward to the distraction of the Champions League, with a trip to Olympiakos coming up on Wednesday, with the club registering their worst start to a Premier League campaign under Wenger’s 16 years in charge.
"It's good for us we have a Champions League game three days after [the Swansea defeat] and we have something to focus on," said the Poland international. "We were obviously frustrated and disappointed after the game but now it's about Olympiakos and we will do our best to move on.
"The players give 100 percent in training and on a Saturday afternoon. I didn't say the players didn't want it enough. I'm definitely surprised by our position in the league. When you look at the quality of our players we should be fighting for the league.
"We have one of the best teams in the league, but it's our responsibility to put things right. What's gone wrong? That's not for me to say."