Foster was thrown straight in from the start less than 24 hours after joining on a season-long loan from Blues - and he pulled off some vital saves to keep the Robins at bay.
"I recognised a Premier League goalkeeper in Ben, a goalkeeper who has been allowed to leave Manchester United," Hodgson told the WBA website.
"I understand Sir Alex wanted to keep him there behind Edwin van der Sar because he is such a good keeper.
"The times he's been let out on loan he's done extremely well.
"So much so that Birmingham City were tempted to pay a lot of money for his signature.
"He was a No.2 goalkeeper at Manchester United and we know a lot about him from playing there and at Birmingham.
"He's just the type of goalkeeper we need and it's a happy day for me because this is the second time since I joined in February that we've kept a clean sheet.
"Clean sheets are something I don't know anything about!"