Arsenal were knocked out by Southampton in the quarter-finals at the Emirates Stadium on Wednesday by Southampton - who booked their place in the semi-finals with a 2-0 win.
Wenger made 10 changes to the side beat Bournemouth 3-1 in the Premier League last weekend but Keown said there was enough quality in the Arsenal side for them to get past the Saints.
Arsenal manager Arsene Wenger
In his Tackle Keown column for the Daily Mail, Keown said: "The defeat by Southampton will have been worrying for Wenger as the players didn't seem to have any desire.
"There was enough on the pitch for Arsenal to win that match. Francis Coquelin and Mohamed Elneny both started at Old Trafford in the League, Aaron Ramsey has played in the Mesut Ozil role to great effect for Wales and Carl Jenkinson and Kieran Gibbs have both won England caps.
"But there was no urgency to their play. They didn't seem to create anything. It was all very safe, passing the ball in front of their opponents."
Arsenal's Francis Coquelin in action
Keown lists several players that are not exactly unknowns, and he picked out Jenkinson's performance in particular as a worry - suggesting the defender looked 'devoid' of confidence.
The obvious disappointment for Arsenal is that it ends an unbeaten run which goes back to the opening day of the Premier League season when they lost to Liverpool - and this defeat to Southampton means that one possible avenue to silverware has been closed off.
Any defeat where the side looks completely off their game is going to be worrying for the manager. November hasn't been a month that has exactly been littered with victories but he will want a positive response from his players the next time they are given an opportunity.
Arsenal's Carl Jenkinson in action with Southampton's Sofiane Boufal