Hodgson now takes charge of England after defeat to Arsenal yesterday.
"Roy has given the club a stability and structure on a daily basis, making players better as individuals and as a team," Downing told the WBA website.
"He has improved the standard by working with professionalism every day. I know every manager does that but he is making players, whether they're 30 years of age or 20, better.
"There are a lot of players in the dressing room pleased with his achievement but very disappointed he's gone. But we have the foundation there now to move on next season.
"He's left a legacy and you saw the appreciation from the supporters.
"We're all very hopeful he can do the same for England."