Losing 2-1 at home, Arsenal were almost down and out at 3-1 when James Vaughan raced through on goal, only to be denied by Manuel Almunia. Everton had played on after Denilson fell to the turf due to pains in his side.
As no foul was committed, and the midfielder had not suffered a head injury, referee Peter Walton did not have the power to stop the game, which eventually finished 2-2 thanks to an injury-time equaliser from Tomas Rosicky.
Wenger has told the Brazilian that to prevent Arsenal being caught on the break in future, next time he should deliberately commit a handball to concede a free-kick.
"No. I wasn't [upset that Everton played on]," Wenger told the club's official website. "I said to Denilson afterwards: 'If that happens [again] you have to commit a handball.'
"I'm very serious. If you go down, and there hasn't been a foul, you cannot ask Everton to stop their counter-attack and not to score. So, if you go down like that, at least put your hand on the ball and it's a free-kick."
Meanwhile, young midfielder Fran Merida has dismissed suggestions that he has already agreed a pre-contract with Atletico Madrid that would see him return to Spain in the summer.
Wenger has admitted his concern at a lack of progress in talks with Merida but the player insists he has not yet taken a decision over his future.
"At the moment I'm in talks with the boss," he told the club's matchday programme. "My agent and I are only talking to Arsenal at the moment and nobody else."