The Croatian's tenure at the London Stadium was brought to an end earlier this month following a run of two wins in their opening 11 Premier League matches of the season, a sequence of results that currently leaves them in the relegation zone.
Bilic did enjoy some good times with the Hammers, helping them to their best ever Premier League points tally during his first season in charge, and vice-chairman Brady has now revealed it was an extremely tough decision to sack the 49-year-old.
Writing in The Sun, Brady said: "He was an honest man with integrity and intelligence and was furiously loyal to West Ham. So sacking this thoroughly decent man was one of the hardest things our board felt it had to do in 25 years in football."
David Moyes has succeeded Bilic as West Ham boss and Brady has backed the Scot to be a success despite previously criticising him for comments he made towards a female reporter during his time at Sunderland last season.
Brady continued: "A few months ago I highlighted that the then Sunderland manager David Moyes gave an unworthy reaction to a question from a woman reporter. He apologised to her and I welcome his move to us and know he won't make such a remark again."