The Germany international made an instant impact following his club-record move from Real Madrid in September, and has helped Arsenal to the top of the Premier League table.
However, he has scored only four league goals this season and has not found the net since December 8.
But Wenger feels fans can be guilty of demanding too much from the 25-year-old, especially when it comes to scoring goals.
"Sometimes people expect him to make the difference alone," the Frenchman told Arsenal's official website.
"Sometimes when it doesn't work you expect him to take the ball and put it in the net. He is more a passer than a finisher.
"(Goalscoring) is one of the things he can add to his game for sure. It doesn't need to be criticised, it needs to be encouraged.
"He is 25, he can only get better. The best years are coming for him now."
Arsenal confirmed on Monday that Wolfsburg assistant manager Andries Jonker will become the head of their academy in July, replacing the departing Liam Brady - news that has been welcomed by Wenger.
"I am very pleased that Andries is joining us," he added.
"He has a big reputation in the game and was a key part of the team which developed the structures which are now producing such strong young players in Holland.
"I look forward to working with him. I would also like to thank Liam for his work which has been outstanding over many years."
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