The 21-year-old was expected to be named in Fabio Capello’s final World Cup squad but failed to make the cut as the Italian preferred to take Shaun Wright-Phillips and Aaron Lennon.
Keown says that although Walcott has the pace to beat a player, his decision making is poor and also criticised Wenger for not helping him recreate the form that saw him star for England under Capello.
"He runs at a frightening pace, he is rapid, but when he gets into those positions he is not able to think quickly enough, does he pull it back, does he shoot or does he go on his own?" Keown told BBC Radio 5 live.
"His decision making is the problem, he hasn't been able to do that.
"Under Capello it seemed as if he has been getting it right in the main, under Wenger, no, there has been a problem, whether or not that is the coaches' fault, it has to be the players, he has just not played enough games.
"He has become a bit of a one-trick pony in terms of going for the line. People just double up on him.
"When he has got time and space then he finds it a problem and he has got to sort that out with his game."
Walcott joined Arsenal from Southampton in January 2006 and former England winger Chris Waddle, who launched a scathing attack on the Gunners star earlier in the season, is not surprised he has not been included in the final 23 for South Africa
"Since I first saw him at Southampton till today, he has never changed his game in my eyes," said Waddle.
"I have nothing against him but it's no surprise to me he's not on the plane."
Become a fan of Goal.com UK's Facebook fan page for all the latest news and insight into everything related to the beautiful game!