Wilshere struck once in each half, the first an exquisite finish after escaping down the right wing, to fire the Gunners to a 2-0 Champions League victory at the Emirates Stadium.
The strikes lifted his total for the season to four and Wenger, who recently expressed doubts that Wilshere would be a regular scorer, insisted Ramsey's 13-goal haul this season has motivated his fellow midfielder.
"I have nothing against Wilshere scoring - if I'm wrong I'm happy! I liked his first goal because before he'd rush a little bit," the Arsenal manager said.
"He's starting to think 'what Ramsey can do, I can do as well', the first goal shows that.
"What Ramsey has done puts in Jack's mind that he has to score as well. If you're a midfielder you want to score goals."
Wilshere's opener arrived after just 29 seconds but Arsenal had to wait until the 66th minute for their second when the England international tapped in Mesut Ozil's delicate pass.
"We were in control of the game overall and I never really felt that we were under threat," Wenger said.
"Sometimes we were missing the cutting edge to finish the game off early on, but we were so much in control that we felt that would come. It came a little bit late for my taste, but it came."
Arsenal sit at the summit of Group E on 12 points but have yet to confirm their place in the knockout stages of the Champions League.
Borussia Dortmund and Napoli could yet progress instead, although the Gunners only need a draw in Naples on December 11 to guarantee they will progress and could even lose and still advance.
"It's unbelievable that we have 12 points and still have to finish the job, but that's reality," Wenger said.
"It's a tricky situation. In over 150 Champions League games this is the first time I have seen this.
"It would be a mistake to think we just don't have to lose big. We have to play in a positive way and try to win the game, anything else will be a gamble.
"I will have to play a full-strength team against Napoli, I can't take any risks.
"We have three Premier League games before then so I have to use the squad well to make sure we don't drop points in the league and go to Napoli with a strong team."
Wenger was unhappy that midfielder Mathieu Flamini had cut the sleeves of his jersey short, saying: "I was surprised, he won't do that again".
He also refused to condemn Ozil for missing a lazily-taken first-half penalty.
When asked about the German playmaker's spot-kick, Wenger replied: "That's good news for England maybe.
"Everyone can miss a penalty. His run up to the ball was short, but that's the way he takes them."
Source: PA
Source: PA