Arsenal 3 Burnley 1: Walcott answers his critics while Burnley suffer
Walcott, who turns 21 later this month, had come under fire following his midweek outing for England, when he was replaced by Shaun Wright-Phillips after a largely ineffectual display.
However, the Arsenal winger produced the goods as his fine second-half finish helped the Gunners close in on the top of the Premier League, moving level with leaders Chelsea, although having played a match more.
Wenger said: "Theo Walcott gave you the great response you waited for.
"He does what a player has to do – not talk in the newspapers and let your performance talk on the pitch.
"He didn't answer any critics other than with a good performance today and that's what you want from a player. That shows he is mentally strong."
Arsenal should have been out of sight when Burnley equalised at the start of the second half through David Nugent.
Nicklas Bendtner was the main culprit – the Dane missed a string of chances in the six-yard box. Substitute Andrey Arshavin made the result secure in stoppage time and Wenger said: "It could have been four, five or six but as well they had a chance to make it 2-2 after a corner.
"In the end you are happy when you miss the chances we missed today, but you get the three points."
The events of the previous weekend at Stoke were still on the minds of Arsenal fans as they chanted Aaron Ramsey's name before kick-off, while a large banner was also displayed in support of the promising Wales international, who will miss the rest of the season with a double broken leg, while the players wore 'Get Well Soon Aaron' T-shirts during the warm-up.
There was one flashpoint when Walcott squared up to Daniel Fox following a sliding challenge by the Burnley man.
But Burnley manager Brian Laws, however, felt there was little cause for concern from the challenges in the match.
He said: "Arsenal cannot have it all their own way. We have got to make challenges at some stage in the game. I have seen the frustration from Arsenal, but you cannot take away tackling. It is part of the game."
Laws believes his side can take heart from the performance.
He said: "We responded much better in the second half when we stepped up 10 yards and asked questions.
"After the goal, we looked comfortable, but Arsenal are going to create chances and our goal lived a charmed life at times.
"This was never going to be the match which would decide our future in the Premier League, it is always going to be decided at home, more than anything.
"The fact we stayed in this game and frustrated Arsenal for long periods suggests we are going in the right direction and I believe we will get that result away from home sometime."