However, the Arsenal winger produced the goods on Saturday 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 and that's what you want from a player. That shows he is mentally strong.
"I was quite sure he would respond with a good performance but you never know, it affects you when you get criticised. The way he answered that at his age is remarkable."
Wenger, though, admitted the loss of Cesc Fabregas was a concern, the skipper leaving the field just after he had fired Arsenal into the lead.
"He has a hamstring problem and how big the damage is we don't know yet because it's too early.
"We have to make a late decision over whether he plays on Tuesday, certainly. It is the same hamstring [he hurt earlier in the season]."
Arsenal should have been out of sight even 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, but you get the three points."
The Arsenal manager added: "I believe on the surface he looks like 'okay, I missed the chances', but underneath he is really disappointed.
"In his finishing, he missed chance after chance, but if you are a striker, it is like that. You think 'I missed the first one, but I will score the next one'.
"Once you have missed the second one, you are in trouble because after you do not know how to take the third one - do I really go for it, or wait for the ball? That is what happened to him today."
The events of last 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.
Wenger said: "In the first half, when we went into the tackles, it was still in our heads a bit."
Burnley manager Brian Laws, however, felt there was little cause for concern from the challenges in this encounter.
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."
Laws added: "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."
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