Hodgson will lead his country into Euro 2012 battle this summer having accepted the Football Association's offer of employment as Fabio Capello's successor. However, he will do so with the Baggies looking for a replacement from a position of strength after finishing their second season back in the top flight in 10th place.
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."
The midfielder added: "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."