The Gunners have been questioned in the past about not being up for the fight required to win silverware on a regular basis.
They welcome Manchester City to the Emirates Stadium tonight looking to boost their title hopes having already seen off fellow top-four sides Leicester and Manchester United with relative ease this season.
Having lifted the FA Cup for the past two years Arsenal ended a barren spell without trophies and are right in the title picture once again.
A 3-0 victory at Olympiacos also saw them progress into the Champions League last 16 — where they will meet Barcelona — and Wenger feels recent results are showing his players are answering the critics in the right fashion.
“We have to accept that’s part of it but we have to give our answer on the pitch week in, week out, and the doubt will slowly die,” he said.
“It was true for a while because we were a young team and a young team can be up and down. But I believe now we have shown that what we did at Olympiacos is not a team of no character.
“You need to be special to achieve that. We won the FA Cup in the last two seasons and you need character to win the FA Cup. Everybody would love to do it every year.”
Wenger feels consistency is the main proof of character and his team need to show that over the festive period to prevent themselves slipping away in the new year.
The inability to put together a largely consistent season is one of the reasons Arsenal remain without a title since 2004 but, having gone to high-flying Leicester and won 5-2, Wenger has backed his current crop to turn that around.
He said: “We are the only team who have beaten Leicester basically, and in a convincing way. The character is down to consistency in life.
“That’s what I call character. All of us can be for one day in our life exceptional but character is to have a target and maintain your focus on that target.
“That’s what I call character and that’s what we have to show in the league.”
Wenger has not ruled out talismanic Chilean Alexis Sanchez recovering from a hamstring problem in time to return against City.
The former Barcelona forward, as well as club-record signing Mesut Ozil, have been in fine form for the Gunners this season while Olivier Giroud continues to confound his critics having scored 27 goals in the calender year.
In the past, those types of names could have been tempted away from north London, with City flexing their financial muscles over Arsenal on several occasions.
Emmanuel Adebayor, Samir Nasri, Bacary Sagna and Gael Clichy have all left the Emirates Stadium to join City in recent seasons but — now they are on a better financial footing themselves — Wenger insists the club can decide whether players will leave or not.
“That was difficult at the start to take but we had to survive financially and we had to live with it,” he said when asked how it felt to lose key players to the Etihad Stadium.
“We are in a much stronger position now. I cannot say it will never happen again because you never know but we are in a position today where we have not to give in.”
Meanwhile, City playmaker David Silva has stressed that he and his team-mates are “very happy” with manager Manuel Pellegrini and focusing only on the present.
Pep Guardiola is again being heavily linked with City after announcing that he is to leave Bayern Munich when his contract expires at the end of the season.
Pellegrini insisted last week such talk did not bother him and Silva claims the players will not be affected.
The Spaniard said: “We are all very happy with Manuel and it is not something we look at. We look at the day today and not what is going to happen in the summer.”
City — who won the Premier League and Capital One Cup under Pellegrini in 2014, but nothing last season — are currently third in the table, one point behind Arsenal.
Tonight’s game could prove critical to the title race and although Silva has emphasised the contest will not “define” anything at this stage, he has no doubt Arsenal have “everything they need” and — along with surprise package Leicester — are City’s “direct rivals”.
The 29-year-old has also expressed his admiration for Wenger’s dynamic side, and admits if City do not win the league, he would be happy to see the Gunners take the title.
“You always feel more attracted to people who play the way you play,” said Silva.
“If we don’t win it and Arsenal win it, it will be good. But we are here to win it ourselves.”