The midfielder is a big fan of the new England coach.
Andrews, who will also be at Euro 2012 with the Republic of Ireland, said: "I am delighted for him personally, but selfishly probably, the players at West Brom were disappointed he left.
"He has been fantastic for the club. He has really established it into a proper Premier League football club, whereas in years gone past it's had that label of a yo-yo club.
"But now even with the calibre of applicants for the job, it shows what a good job he has done.
"People will be applying now thinking it's a stepping stone maybe to bigger and better things."