Wilshere admitted a retrospective misconduct charge after television cameras showed the England international raising his middle finger in the direction of Manchester City supporters during the second half of the 6-3 Barclays Premier League defeat at the Etihad Stadium last weekend.
The Gunners submitted mitigating circumstances to the FA, arguing the length of the mandatory punishment was excessive, with Liverpool striker Luis Suarez suspended for only one match following a similar incident in December 2011.
However, a precedent had been set earlier this season when a two-match suspension was handed out to Blackpool winger Tom Ince after he was retrospectively charged in relation to a gesture towards a match official in a Capital One Cup tie against Preston, and so the ban was upheld.
Wilshere will now miss both the visit of Chelsea on December 23 as well as the Boxing Day trip to West Ham.
While Wenger understands Arsenal have little choice now but to take the punishment, the French coach feels referees should follow the letter of the law when confronting all instances of indiscipline.
"We thought the ban was one game and that is why we appealed. It is two, we have to accept it and to swallow it," Wenger said.
"He was wrong in his reaction, but we are now in a situation where we have to accept it and wait until he comes back and focus on our next games without him.
Wenger added: "Do you want unfair behaviours to be punished? Yes.
"The players adapt, they are intelligent people. They always test the border, how far can I go? They look at others and see how the referee responds and they adapt.
"If the referees are consistent in doing that, they will stop it but you want consistency."
Arsenal will need consistency on the pitch if they are to avoid a promising start to the season evaporating before the turn of the year.
Should results go against them this weekend, Arsenal could be down in fourth, and only one point ahead of Everton.
Wenger is in no doubt his side can come out of last weekend's drubbing at City with a positive reaction.
He said: "Quite amazingly, despite the fact we conceded goals (the Man City match) was not all negative because we could have scored six as well, so on the offensive front we have shown that we have huge potential.
"I believe that we should come out of that game even stronger in our belief, even stronger in our resolute attitude, because we have shown until now that we can be very strong defensively, and as well on the day we have shown that we can be dangerous against anybody.
"We can rectify the defensive problem, but that's what we want to show against Chelsea."
Defender Laurent Koscielny is an "80/90 per cent" doubt for Monday night's showdown with Chelsea after he suffered a deep gash in his knee just before half-time at the Etihad Stadium.
German forward Lukas Podolski, however, could be involved for the first time since late August following his recovery from a hamstring tear.
Wenger said: "It is a big boost because he can score goals in big games.
"He has shown that before. He is a clinical finisher and a great football player."