Walcott created Thomas Vermaelen's injury-time winner for the 2-1 triumph.
Wenger said: "He was outstanding from the first to the last minute. It's one of the best, best games I've seen of Theo because I felt tonight he had absolutely everything in his game - combined well, crossed well, was always in the game.
"He's making good progress; he's an intelligent boy. People forget he is very young - 23 years old."