Wenger felt winger Sterling dived for the penalty that put Manchester City 2-0 up in Sunday’s win over Arsenal.
“I believe it was no penalty,” Wenger told BBC Sport. “We know that Sterling dives well, he does that very well.”
Shearer said on Match of the Day 2: “There is no way that was a dive and it was a penalty.”
The ex-England captain added: “It’s one thing for Wenger to deflect from his team’s inadequacies, it’s another to question someone’s integrity and be wrong.
“I think he owes Sterling an apology.”
City’s win – their ninth successive league victory, a club record for a single season – saw Arsenal slip to sixth in the Premier League table, 12 points behind the leaders.
Wenger was also “upset” by City’s third goal, when both Gabriel Jesus and David Silva could have been flagged for offside.
The Frenchman claimed the standard of refereeing is getting worse every year.
“I feel the referees don’t work enough. The level drops every season at the moment and, overall, it’s unacceptable,” he said.
“The third goal was offside. I am very upset because at 2-1 we were in the game.
“The third goal was the killer and it is by coincidence that mistakes always go for the home team, as we know. You can accept it if City win in a normal way, but this is unacceptable.”
Manager Pep Guardiola declined to discuss the decisions that went for his side.
“We won in the best way,” the Spaniard said. “Sometimes it’s like this.
“I was told it was offside and I don’t want to win like this, but earlier this season Arsenal beat Burnley with a handball in the 96th minute.”
Ex-Gunners striker Ian Wright, also appearing on Match of the Day 2, agreed with Shearer’s view on City’s penalty.
He said: “It was a penalty, the defending was poor. It was clumsy and clunky from Nacho Monreal and he catches a leg. You can see it clearly. It’s harsh for Wenger to say that, it’s not good.”