Wenger is grateful Adebayor did not follow Kolo Toure, Emmanuel Eboue and Alex Song to the African Nations Cup after Togo failed to qualify.
The Arsenal boss declared: "In the past, he has sometimes ended up going out to the flanks because he so wants to be involved in play - but that drags him away from where he can be lethal.
"We have been telling him that for a while and he was more focused on being central today which is good.
"He has an unbelievable jump, he times his jumps very well and he's terrific in those situations."
Wenger quipped: "I must confess I wasn't devastated when Togo didn't qualify.
"It would have been difficult without Adebayor although we do have players who are coming on very well like Eduardo, (Nicklas) Bendtner and (Theo) Walcott.
"He has personality and he is now focused on his achievements here.
"He is also the main striker now and he gives us an added dimension with his headers."
Croatian forward Eduardo had moved out to the left in the second half, and it was his run and centre which lead to a third, when Tomas Rosicky volleyed in from close range with nine minutes left.
Wenger said: "We were in control for 90 minutes. We gave a strong response, scored early goals, kept things tight defensively and were technically very good.
"It shows that the team wants to do it this season, especially after a disappointing result last week against Birmingham and that they can come back in a very strong way."
Wenger added: "We scored three goals from crosses, which is quite unusually for us - but that shows we have a variety now in our game which allows us to deal with any kind of resistance we get."