The club captain, he was sold to bitter rivals Chelsea after the club's relegation on a record 42 points in 2003, a side regarded the best to ever be relegated in terms of personnel.
Cole returned for a second spell under Sam Allardyce in 2013 but was rarely used and suffered with injuries before being released to join Aston Villa.
Hammers fans have had to suffer in the interim with another relegation in 2011 under Avram Grant while also watching their golden generation sold off and enjoy success with their Premier League rivals.
Under new boss Slaven Bilic the Irons have officially enjoyed their best ever season in the Premier League era and have a positive goal difference for the first time since 1986 as they battle for a European spot.
'Glenn wanted three signings... he got none'
"The squad was so thin," Cole told Sky Sports' Fantasy Football Club.
"Glenn wanted Les Ferdinand at the start of the season, he came in January, and I think if he'd have come at the start of the season we would have stayed up because he would have given us that experienced prescence.
"He wanted to bring in (Didier) Drogba as well from Guingamp, but they (then West Ham owner Terence Brown) wouldn't do that deal, god, the history of football would be different if that would have happened.
"And he was even talking about (Pep) Guardiola (then a holding midfield player surplus to requirements at Barcelona)... and he got no-one."
West Ham had finished seventh the season before under rookie boss Roeder and looked a club on the up with the likes of Cole, Michael Carrick, Jermaine Defoe, Glen Johnson, Trevor Sinclair, Paolo Di Canio and Fredi Kanoute in their side.
So it's a sobering thought for Hammers fans that the addition of a then relatively unknown goal machine like Drogba and two experienced heads in Guardiola and Ferdinand could have prevented them having to enjoy such a turbulent 13 years since.
The West Ham faithful had long been calling for Brown and his board to leave the club for a continued lack of investment, ambition and vision.
And Cole's comments only add further weight to those sentiments.