The Gunners moved clear at the top of the Barclays Premier League with a 4-1 victory over Norwich at the Emirates Stadium, where Wilshere finished off a sublime passing move around the edge of the penalty area to set the home side on their way.
It was an 11th win in all competitions for Wenger's men since they lost on the opening day of the season to Aston Villa and has led to talk of a sustained challenge for honours.
Wenger maintains consistent performances at such a high level will hold the key to realising those ambitions.
"We have room for improvement - and being in the position we are in at the moment and knowing we have room for improvement is of course a good feeling," the Arsenal manager said.
"The 'feel good factor' is down to the quality of the spirit of the team, the solidarity of the players, and their desire to do well.
"We know we are a team that looks like being successful - for that you need a special hunger and I believe these players have a special hunger."
Wenger continued: "I believe in life you can always improve and that is what makes a top-level sportsman or a top-level team, is they always have that surge for improvement.
"I believe that collectively in the way we win the ball back and the use of the ball offensively, we have room for improvement, for more consistency in that and that is what you want from the players."
Arsenal will tackle last season's European runners-up in a double-header on matchday three and four which could well shape the outcome of Group F.
The Gunners are currently top by three points following back-to-back wins over Marseille and, most impressively, Napoli.
"It is not a decider, but it is an important one," said Wenger.
"It is an 80 per cent game for me, for the qualifier.
"If we win the game and we win the other home game, we know we are there.
"The German teams, they have a desire to play, they play with a positive attitude and they have produced as well many good players recently.
"They don't hide, we don't hide, so it should be an exciting game."
Arsenal will rest midfielder Mathieu Flamini as a precaution following a concussion he suffered during the Norwich match.
England forward Theo Walcott remains sidelined following a minor setback after surgery on an abdominal problem.
Wenger indicated he would rotate the starting XI somewhat, given the amount of matches facing his squad.
However, the Arsenal manager expects nothing less than full-on commitment once again when they tackle Jurgen Klopp's well-drilled side, which will be spearheaded by Poland forward Robert Lewandowski.
"What is important is that we go into the game and focus on our quality, on our performance. For me that is more important than focusing on Dortmund," Wenger said.
"[We want to] come out of the game and feel that we have played at our best - if we do we will be difficult to handle for everybody."
Goalkeeper Wojciech Szczesny has produced some consistent displays in Arsenal's resurgence.
The Poland stopper - who played well at Wembley last week despite the 2-0 defeat by England - feels he has grown from the experiences of last season, which saw him dropped for the Champions League away game against Bayern Munich.
"Looking back now it was a good lesson for me, one that I needed at the time," Szczesny said.
"I definitely have got sharper since then, I have worked harder in training.
"It worked back then for me and I have carried on doing it.
"I am feeling like I am a bit more consistent at the moment.
"I am trying to do the same thing all over again and it seems to be getting the best out of me."
Szczesny added: "I would have preferred a few more clean sheets, but I am just delighted with the team's form, how we have been playing and getting the results."