The midfielder was spared an ejection after a cynical challenge on Theo Walcott as the Toffees frustrated the Gunners at the Emirates Stadium for a result that did few favors for either team's Champions League hopes.
Wenger felt that referee Chris Foy was too lenient on the visitors for their physical approach but remains satisfied with the north Londoners' position in the top-four race.
"We should have won the game," Wenger said. "It keeps us in a strong position in the race for top four.
"The game was intense physically but I felt in the first half the ref didn't deal well with the intimidating challenges. We responded well and we had a fantastic commitment.
"Their tactics were detrimental to the fluency of our game. Yes, [Gibson] should have been sent off.
"I never speak to the ref. You should ask the ref why he wasn't [sent off]. He should have had a yellow card even before the first challenge.
"You must respect Everton for the fight they put in. They decided to make it physical. Sometimes they went over the edge but it's up to the ref to make the right decisions. Protecting is a big word; it is just up to him to make the right decisions.
"I do not want to comment on every decision the game is what it is. Despite that we had the chances, we can only look at ourselves. We are on a very strong run so we don't want to complain too much, let's look at ourselves."
Chelsea and Tottenham could now overtake Arsenal's 60 points should they win their games in hand, but Wenger is confident that his side will reach the Champions League.
"If we win our coming games we'll get there. Others have 58 with games in hand but they play each other," Wenger said. "We must not leave it so that we depend on others. My belief is strong, and I'm confident we will do it and the best way is to put the same effort into the next game."