City scored their first ever win at Tottenham Hotspur on Friday night with a 1-0 victory to qualify for the fifth round of the competition.
Nathan Ake scored the only goal of the game after 88 minutes after Vicario failed to hold a Kevin de Bruyne corner.
Ruben Dias stood in front of the Spurs goalkeeper but Tottenham’s claims for a foul were rejected.
Former Manchester United captain Keane was not convinced Vicario had been fouled and insisted the Italy international had not “controlled his area”.
“A goalkeeper has to control a six-metre area,” Keane told ITV Sport.
“A goalkeeping coach I worked with years ago said – and I liked this – that you have to be violent. You come and attack that space and get people out of the way. You have to let them know you are there. If the defenders are coming back to you, be physical. Clear the area.
City failed to trouble Spurs in a series of similar corner kicks that led to a goal. Their determination paid off in the end, with Keane believing the defending champions were determined to exploit Vicario, having identified him as the “weak” link.
“They worked on it, they knew he was a weak point,” Keane continued.
“We were disappointed with him too, we thought City would try a couple of shooting angles but they persevered and scored in the end. They looked at that goalkeeper and said to themselves, ‘Right, he’s going to be weak in that area’.”
Spurs boss Ange Postecoglou, meanwhile, decided not to challenge the referee’s decision to allow the goal to stand.
‘I’m sure it was well looked at and the referee and VAR didn’t see anything wrong. The decision was made and we have to accept it,’ he said.
On Tottenham’s performance, he added: “It was a tough game against the best team. We tried to stay in the game but we scored so late. But they were better.
‘They make you suffer in some moments, so we had to do our best, but for the most part we defended well. It was too tough a test for us.
We are continuing with the way we have been doing things, which doesn’t mean that anything has changed for us today.’