Alain Vigneault already has “a Lincoln Tunnel story.”

Let’s just say it involves a wrong turn by a man living on the upper West Side of a new city.

“I’m embarrassed” Vigneault 52 said last week in his former home of Vancouver.

Living adjustments are normal although especially in the Big Apple. Vigneault’s bigger challenge in his first season as Rangers head coach will be operating without the “clean slate” on the bench that he is preaching for his players on the ice.

Vigneault may be starting over after seven seasons in Vancouver but he has inherited the Rangers’ salary-cap concerns injuries and arena construction that will affect how he manages the team beginning with Thursday night’s regular-season opener in Phoenix.

The coach for example has no choice but to seek a fit on the wing for veteran forward Brad Richards whose $6.7 million cap hit has the Rangers right up against the NHL’s salary ceiling.

Vigneault must coach the first nine games of the regular season on the road as the final phase of the Garden’s three-year renovation project pushes back the home opener to Oct. 29.

Meanwhile he must play the first 10 games without injured top-six winger Carl Hagelin (shoulder) and go without injured captain Ryan Callahan (shoulder) for at least Thursday’s opener against the Coyotes.

So instead Vigneault — or A.V. as the Rangers call him — must entrust Swedish rookie winger Jesper Fast 21 with crucial early shifts and second-year forward J.T. Miller 20.

He must do all of this while replacing the fired John Tortorella who despite his well-documented flaws and overbearing nature achieved significant success with the Rangers in 2012 with a trip to the Eastern Conference finals.

“It’s not about kids or youth” Vigneault said after Sunday’s practice in Greenburgh. “It’s about who can help us win games.”

Those youngsters impressed during the preseason but it will be difficult to get them assimilated quickly. Nothing has been typical or routine yet for the Rangers and it won’t be for the first month.