Arsene Wenger wants his Arsenal side to focus on strengthening their own belief in the quest for a sustained assault on the Barclays Premier League title.
The Gunners consolidated their position at the top of the table by securing a 2-0 win at managerless Crystal Palace, where captain Mikel Arteta was sent off not long after scoring a penalty at the start of the second half.
It was the ideal response from Wenger's men to the midweek Champions League home defeat to Borussia Dortmund, which had seen questions raised about how far Arsenal could go this season.
"It is people who do not believe that we have a chance, but the only thing we can do is win our games," Wenger said.
"The only thing which is important is every win makes you a bit stronger and strengthens the belief.
"We have difficult games coming up, and that will be a good test, but I am confident."
Arsenal had started brightly at Selhurst Park, where England midfielder Jack Wilshere was put on the bench as a precaution after aggravating his troublesome ankle on Tuesday night.
However, the Gunners were made to work for their victory, and there were long spells where Palace pressed the league leaders onto the back foot.
Arsenal's breakthrough came at the start of the second half when Serge Gnabry - on as an early substitute for Mathieu Flamini, who limped off with a groin problem - was taken out by a rash challenge from Adlene Guedioura to concede a needless penalty, which Arteta coolly dispatched.
However, just after the hour mark, the Spaniard was off back down the tunnel when referee Chris Foy brandished a red card after he had clashed with former Arsenal striker Marouane Chamakh some 35 yards out, the pair falling in a heap following what looked like a 50/50 challenge.
Following consultation with his assistant, Foy viewed it as denying a clear goalscoring opportunity and the midfielder must now serve a one-match ban, the midweek Capital One Cup tie against Chelsea he was unlikely to be involved in anyway.
Nevertheless, Wenger still disagreed with the decision.
He said: "It has to be the last man and that is not proven to me - also the foul was not obvious."
Arteta also felt he had been hard done by, telling Arsenal Player: "It was a very harsh decision to send me off. Chamakh kicks my fight foot. I have seen it on television. It is 40 yards away from goal too.
"It is true that I tried to block him with my hand but then he came with his left foot into my right calf and then we were both on the floor. It was never a tackle from me."
Palace briefly rallied as they looked for a positive end to a week which started with a 4-1 home defeat by Fulham that resulted in the departure of Ian Holloway.
Defender Joel Ward saw his shot from 20 yards tipped onto the bar by Arsenal goalkeeper Wojciech Szczesny, who quickly produced an even better save to deny Mile Jedinak from the resulting corner.
It was, though, the Gunners who went on to secure all three points with a second goal on 87 minutes when Aaron Ramsey broke down the left, his perfectly timed cross headed past Julian Speroni by the hard-working Olivier Giroud.
Wenger said: "Crystal Palace put a shift in, they were determined to fight very hard, we needed to be patient and we were.
"Many times now this season away from home we have won the game in the second half because we are mature, do not make a mistake and we do not rush our game."
The full extent of Flamini's injury is yet to be assessed, but there have been suggestions it could sideline the industrious French midfielder - who had missed the Dortmund game as a precaution following concussion - for up to a month.
For Palace, top of the agenda for Monday's debrief will be the search for a new manager.
Caretaker boss Keith Millen, who made six changes to Holloway's final starting XI, feels the Eagles remain an attractive proposition despite the fact they have lost eight of their opening nine games back in the top flight.
"It is a great club in a good financial position with four great owners who really want to achieve something at this club," he said.
"But also when you look at the group of players against Arsenal, people that are interested in the job would look at that and think 'I've got something to work with there'."
"However, the players know if they keep going like that they will get points.
"Whether they can get enough points you don't know, do you? But you have to just work from week to week and enjoy what you are doing."