Sidwell will miss Fulham's last four games of the season after he saw red for the second time in two appearances.
The former Arsenal midfielder, who was given a straight red for a dangerous tackle on QPR defender Armand Traore three weeks ago, caught Mikel Arteta on his standing foot with a two-footed lunge just 12 minutes in to Saturday's London derby at Craven Cottage.
Wenger also ended the game with 10 men after Olivier Giroud caught Stanislav Manolev with a last-minute lunge.
The Gunners boss had no qualms with Giroud's sending off, and that of Sidwell, which he thinks could have caused serious injury to Arteta had it happened a millisecond earlier.
"I think the referee could only give a red card (to Sidwell)," the Arsenal manager said.
"We will see (if Arteta is Okay). He played the second-half. I don't know how much damage is done. It is a kick, a bad kick.
"I don't know if he has twisted his ankle or not. In these kind of things it is a question of a fraction of a second.
"If you are fully on your foot at the moment you get it you break your leg. If you ease a bit off maybe that is why he got away with it."
Sidwell's tackle on Traore - a long sliding lunge while the Frenchman was at full pace, drew widespread condemnation, and the former Chelsea man can have no complaints about his dismissal on Saturday.
Fulham boss Martin Jol admitted the 30-year-old, who has also been booked eight times this season, deserved to go.
"I can't defend him because that would only sound ridiculous," Jol said.
"I was annoyed with him, but he says it is not intentional. He will regret that tackle. It was the first foul that spoilt the game
"I know it was not intentional because he wanted to play. He has just come back from a three-match suspension and now he is out for another four matches again so it was not only disappointing him, but also for us because we had to play with 10 men for a long time so that was more disappointing."
Despite the setback of losing Sidwell so early in the game, Fulham coped admirably, continuing to probe the Arsenal back four thanks to impressive performances from Urby Emanuelson, Eyong Enoh and Alex Kacaniklic.
They were left exposed at the back, however, and Per Mertesacker took advantage of some slack defending from a free-kick to lash home just before half-time.
The Gunners took their foot off the accelerator after the break though and they were left hanging on in the end for the win that moves them back up to third in the Barclays Premier League table.
"It was tight in the end as we couldn't score the second goal," Wenger said.
"I believe we became cautious in the second-half. Our first-half was quite good, we were in control, and we played well.
"I don't know what happened in the second half, whether it was a physical or mental thing
"The final 10 minutes were really nervy. They started to play direct, in the box they had a few dangerous balls and it was difficult.
"Still, it is a very important win for us."
Jol, whose team are nine points above the drop zone, criticised Bryan Ruiz for failing to stop Mertesacker scoring from Laurent Koscielny's knock-down.
Jol said: "Bryan Ruiz is my sixth man at the end of the wall and he was not doing what he normally should do - stay on the inside of the player - so that was disappointing."