Arsenal will end the season again trophyless, though also runners-up to champions, Liverpool.
Writing for BBC Sport, Keown stated: "Being the bridesmaid so often is the worst feeling in football and it takes a special group to come back from having that happen repeatedly, and win.
"I was lucky because I was part of a special group of players at Arsenal, but we still had to work on it.
"In the summer of 2001, Arsene Wenger brought in a psychologist who said to us that we were second best because the statistics proved we were.
"We weren't very happy about that, but then he told us that he did not believe that the statistics were telling the truth."
The players need to respond
Keown also said, "He looked around the dressing room and said we have got World Cup winners in here, and you have all won trophies in the past.
"His message was that there was more under the bonnet, we just needed to find it.
"It was a clever move by Wenger and the parallels in Arsenal's current position means it is something Arteta could try too, but it can't all come from the manager - it is down to the players to respond in the right way."