The Togo hitman sparked a sizzling return from two-nil down as the Gunners won in thrilling fashion.
Adebayor missed a host of first-half chances but netted twice and set up sub Nicklas Bendtner's strike as the visitors blasted Ajax off the park in the last half hour.
The Dutch hosts led 2-0 at half-time with Luis Suarez and Klaas Jan Huntelaar making the most of some woeful defending from William Gallas and Kolo Toure.
He added: "We always create a lot of chances and don't always score all of them.
"But it's difficult to complain when you score three goals. Manu came good in the second half.
"To keep a guy like him quiet for 90 minutes you need some strength. Slowly his physical power took over the match."