The goalkeeper joined the Owls from their Championship rivals earlier this week.
The 25-year-old completed a free transfer to Hillsborough on Monday, and upon reflecting on his time with the Canaries - for whom, he made no appearances before heading out on loan to Chesterfield and Swindon - he admits that the writing was on the wall for his spell in East Anglia from the very early days.
"I went to Norwich but kind of under false pretences. I thought I was in with more of a shot of playing than I was," he told the Star.
Norwich manager Alex Neil
"It was clear from a couple of days of being there that John [Ruddy] was the number one and I wasn't going to get a fair crack at it. It's why I took the opportunity to go out on loan and get games.
"I don't think I was given the chance to show what I can do at Norwich."
Although Kean appears to have looked elsewhere in the hope of securing first-team football, he may face a similarly difficult task trying to break into Carlos Carvalhal's team.
Keiren Westwood was in inspired form last term, and if they had managed to win the play-off final, it would have arguably been him Wednesday would have had to thank as he made several brilliant saves at Wembley, and was only beaten by a stunning strike.
Keiren Westwood was exceptional last season
Meanwhile, Joe Wildsmith proved that he is capable of being an excellent understudy to the Republic of Ireland international. When called upon, the youngster demonstrated why he clearly has a bright future ahead of him, so the Portuguese may be keen to give him more opportunities this coming campaign.
However, Kean brings with him plenty of Championship experience, having previously played for Blackburn in the second tier, so Carvalhal may be confident that he can rely on him if he is required at any stage.