We beat Southampton at the Emirates Stadium, where a horrible mistake from goalkeeper Artur Boruc help set up a 2-0 victory.
The Poland international made a complete mess of his footwork when caught in possession by Olivier Giroud in the six-yard box on 22 minutes.
Arsenal never looked in danger of relinquishing their lead and settled the game with a late penalty from France striker Giroud.
It means the Gunners took full advantage of Liverpool's draw in the Merseyside derby at Everton to move four points clear at the summit, and produce the required response from their defeat at Manchester United before the international break.
"We have a long way to go, but we have the ambition, the focus, the concentration and the desire are there," said Wenger.
"We played against a good Southampton side today who tried to stop us from playing. They did it well and in the end we couldn't take our chances, but we took advantage of their two mistakes.
"Overall you could see why they have played a draw at Manchester United, why they had won at Liverpool because they conceded only five goals until today.
"They are a team who is very well organised and our technical quality helped us to get away with a win today."
Wenger added: "I am convinced that after a break like that, the character is tested. Can you win when you have to in a season like that, straight away again after a big defeat [to Manchester United]? That was really at stake for us."
It was, though, also the sheer hard work and determination of France forward Giroud which helped secure victory, taking his tally to seven Premier League goals.
"Olivier is a positive character who is always ready for a battle," Wenger said.
"He is maybe a little bit, completely different to the rest of the team, that he gives us so much with his physical presence, with his link play which he has improved tremendously. He has the mental qualities and a positive attitude."
Giroud now has 10 goals in all competitions.
Wenger continued: "Other strikers will tell you 'I am not obsessed by scoring goals', but if they don't, they are sick! It is a relief on their shoulders.
"I believe as well that he didn't expect himself to score so many from the start of the season, but it can only boost his confidence."
Theo Walcott came on in the second half, the England forward having been sidelined with an abdominal problem which required surgery.
"You could see he is still a bit short physically, but he has not played at all for seven weeks and only one day training with the group, so that will come back quickly," Wenger said.
Saints boss Mauricio Pochettino, meanwhile, refused to lambast Boruc.
"We were unlucky when we conceded that goal. There is nothing more to analyse. We all saw what happened, draw our own conclusions and we have to just move on," he said,
"I fully support all of my players, these things can happen in football.
"Footballers don't need to apologise to their own team-mates, they can have amazing performances or they can have a bad day as happened today to Boruc.
"The main thing is they all support each other and we need to move forward and keep working the way we have.
"Footballers need to be able to learn from these mistakes. They need to be able to live with these mistakes and know these things can happen, accept them and move on.
"From our point of view, we just offer our complete and 100 per cent support for him, and keep talking to him, working with the entire team and moving on."
Southampton may be the surprise package of the season, climbing into the top four on the back of an unbeaten eight league game run, but Pochettino believes the Gunners are worthy contenders to last the distance.
"After 12 games, Arsenal are playing the best football, so they are definitely candidates to win this league," he said.
Source: PA
Source: PA