The 46-year-old has suggested that had the Saints not been forced to sell some of their best players over the past couple or so years, then they could have been playing in the Champions League.
“The patience of Saints has been sorely tested lately,” West Ham vice-chairman Brady wrote in her football diary in The Sun (Friday, August 21 entry).
“They have been raided to the extent of £125m over the last 14 months and now United are checking up on Senegal’s Sadio Mane.
“Southampton say ‘no chance’ but they said that about Shaw, Lallana, Lovren, Schneiderlin and Co.
"I sympathise because they are being forced to sell and, without all those exits, it could have been the Champions League and not Europa League last night.”
In the summer of 2014, Southampton had to sell Rickie Lambert (Liverpool), Luke Shaw (Manchester United), Adam Lallana (Liverpool), Dejan Lovren (Liverpool) and Calum Chambers (Arsenal).
So far this summer, the Saints have sold defender Nathaniel Clyne to Liverpool and midfielder Morgan Schneiderlin to Manchester United.
If Southampton had been able to retain the services of some of the players they have sold, then they could have had the chance to challenge for a top-four finish in the Premier League.