The 58-year-old was touching on the subject following revelations that Surrey cricketer Tom Maynard was a cocaine user in the three months before he was electrocuted by a live rail on the London Underground.
"Depression remains a definite problem with top sports people," Allardyce wrote in the London Evening Standard. "The rewards they earn are largely irrelevant. In football, for example, you have great highs and terrible lows.
"Those lows can be so debilitating they cause people problems, no more so than managers and coaches. You have to learn to manage those lows without them getting to you too much.
"I would go as far as saying that many managers are suffering from a mild kind of depression based on the kind of job we're doing. Often I have trouble sleeping at night and that's because of the pressure that comes with being a manager."
Meanwhile, the Hammers are preparing to take on Stoke City in the Premier League tomorrow.