The pundit was speaking on ITV Football and did not mince his words when asked to assess the Gunners' performance:
He said (via MailOnline's Sam McEvoy):
"I think Arsenal are a great example on how not to start a game of football. We can talk about being a shambles, but they're so slow out of the blocks—poor attitude.
"The manager summed it up. No energy, no desire, you're looking for your senior players to lead by example.
"I always think, when Wilshere's your captain, to me, probably the most overrated player on the planet.
"And they got lucky with the result at the end of it. But if you start a game slowly, no matter how good you are, it's hard to get going. You can't just switch it on and off."
Arsenal progressed to the round of 16 thanks to their 3-0 victory over the Swedish side in the first leg, but until Sead Kolasinac scored just after half-time at the Emirates Stadium on Thursday, they were in danger of seeing their lead evaporate.
Positive performances from Arsenal players were hard to come by, but Wilshere was particularly disappointing.
Football.London's Charles Watts recorded a moment in which he failed to impress:
Manager Arsene Wenger defended Wilshere in response to Keane's comments, though he conceded the England international did not play well.
"It's very difficult. I personally rate Jack very highly. After that you can have opinions," Wenger said, per the Mirror's James Whaling. "Jack was in a team last night that didn't perform well. Was it one of his best performances last night? Certainly not. But Roy Keane knows that can happen to everybody."
Wilshere admitted to BT Sport after the match the Gunners had "underestimated" their opponents, adding (h/t MailOnline's Jaime Wright): "Yes [they deserved the win], especially in the first half. We were nowhere near good enough. And to be honest, we improved a bit in the second half, but we still weren't good enough."
Former Premier League player Jay Bothroyd agreed with Keane's assessment of Wilshere:
Jay bothroyd @jaybothroyd
Roy was one of the best CM played with some of the best, I believe him. https://t.co/q0RtCNO5kv via @YouTube Ramsey is a better player and I don’t think he can be a starter for England, he couldn’t play regular for Bournemouth but afc fans say he’s the best British midfielder?
The 26-year-old has been the subject of enormous hype from a young age, and even if he had not spent much of his career dealing with injury problems, it would have been difficult for him to live up to the expectations that have been placed on him since he was a teenager.
He's a superb player who can produce moments of brilliance when he's on form, though—he can surge past opponents with the ball, dictate proceedings and split open a defence with an incisive through pass.
Wilshere is right to be disappointed with his and the team's showing on Thursday, particularly given the importance the Europa League should have for the Gunners as their best chance of securing UEFA Champions League football for next season.
If he gets the chance to play in Sunday's Carabao Cup final, he should feel he has a point to prove.