Upson joined West Ham this week.
Brady revealed in a column in The Sun: “With Upson in the team the manager believed we had a better chance of promotion to the Premier League than without him.
“This might not show up in an analysis of the statistics so far this season.
“Before he returned after a year out through injury, the team were close to setting a club record for consecutive clean sheets.
“But in the Premier League, Upson has proved to be a top-class player and replacements of his experience and quality are so difficult to find even Chelsea have been scratching around.”
Brady added: “Had Chelsea pursued their interest in the player, I think most of us here would have said ‘Goodbye’ and wished him well.
“That went for Jermaine Pennant when he left last summer for Liverpool.
“But the Hammers aren’t top four material or anything like it. This week they are Ugly Betty.
“I wish Matthew well at Upton Park and I’ll give him a wave if we pass them by.”
