Defeats for play-off rivals West Ham and Reading leaves the Blades with a mathematical chance of reaching the play-offs but with a hugely inferior goal difference they will be playing in the Championship again next season.
United were stunned when Millwall went ahead in the fifth minute. Former Fulham striker Barry Hayles, who had a brief stay at Bramall Lane earlier in the season before heading back down the M1, picked out Paul Ifill. He found the unmarked Morris who swivelled before stabbing the ball into the bottom left-hand corner of the net.
United should have levelled three minutes later. Danny Webber unselfishly passed to teenager Jonathan Forte whose low angled 12-yard strike span wide of the far post.
Andy Gray glanced a header the wrong side of the woodwork before firing in a teasing cross from the right. Webber lunged and missed and Forte, charging in at the far post, failed to connect from close range.
Millwall had to readjust in the 26th minute when Hayles was stretchered off after a collision with United keeper Paddy Kenny, Ben May stepping into the firing line.
Republic of Ireland midfielder Alan Quinn almost hit the target with a free-kick that dipped over stand-in keeper Graham Stack's head and skipper Phil Jagielka's fierce strike flew across goal as United battled for an equaliser.
Millwall, soaking up a lot of pressure, almost came unstuck just before half-time when they failed to cut out Michael Tonge's cross but as Jagielka stretched to meet the ball, the unsighted Stack somehow smothered the shot on the line.
Marvin Elliott hit the post before Tonge headed a good chance wide late in the game and, with just minutes remaining, Jagielka saw his close-range header smothered on the line.