The winger struck his first goals since returning from injury as the Gunners ran riot after half-time.
They had been handed a fortuitous lead just before the break thanks to a Tim Krul own goal before Walcott struck twice either side of fellow returning forward Nicklas Bendtner’s strike.
Wenger was happy to see them both get through the full 90 minutes and lavished praise on Walcott.
“Walcott is more composed in front of goal this season. His first touch is better. He is an intelligent boy and because of that he will always improve,” Wenger said.
“He was flying at the start of the season and now he is just coming back from injury.
“You can see today that he is ready to go to another level.”
Wenger added: “You are always happy when your strikers score.
“They got through the game without injury and now physically they have a couple of days to recover.
Arsenal’s night was soured by a knee injury to full-back Kieran Gibbs, who went off before the break.
Asked if it was serious, Wenger said: “We hope not. It’s a knee, we hope its not a twist of medial ligament.
“I’m cautious. The way he walks now doesn’t look too good.”
Walcott believes Arsenal will end their five-year wait for a trophy if they can continue to produce the same type of performance that saw off a Newcastle side that beat Chelsea in the previous round.
“People may say that this is a Mickey Mouse cup, but we want to win trophies,” he said.
“We want to look back on the trophies we have won in our career.
“At the moment it’s none, but if we keep playing like that I’m sure it will come.”
He added: “I’ve come back from some long injuries before and it’s nice to get some game time again. It’s nice to be back playing with lads.”
NEWCASTLE: Krul, Perch, Williamson, Kadar, Ryan Taylor, Routledge (Gutierrez 56), Guthrie, Smith (Barton 71), Vuckic, Lovenkrands (Carroll 57), Ranger.
Arsenal: Szczesny, Eboue, Djourou, Koscielny, Gibbs (Sagna 19), Denilson, Eastmond, Rosicky, Walcott, Bendtner (Emmanuel-Thomas 84), Vela (Fabregas 70).
Referee: Andre Marriner (W Midlands).