The Hammers, who are already without the suspended Hayden Mullins for the final against Liverpool, lost 16-goal Ashton after just 22 minutes of the clash with Albion.
It was the second blow to hit United boss Alan Pardew at The Hawthorns as winger Matthew Etherington pulled out before the game after suffering a minor groin problem during the warm-up.
While Etherington should be fit for the final the doubt over Ashton has put 40-year-old Teddy Sheringham on alert to start at the Millennium Stadium.
Sheringham replaced Ashton against Albion and showed enough silky touches to show he remains a threat.
Reo-Coker sealed United's success three minutes before half-time to condemn Albion to their ninth defeat in 12 games - during which time they have collected just three points from a possible 36.
Albion had enough chances to win the game against a weakened United side only to be undone by what has been their major problem all season - a lack of goals.
They should have been well in control before Reo-Coker struck but ended up drawing a blank for the fifth time in six games.
Albion were determined to give their suffering fans something to cheer after their return to the Championship and opened brightly.
But Kanu fired over the bar in the seventh minute after collecting a misplaced pass from Christian Dailly before Nathan Ellington headed a Jonathan Greening cross wide two minutes later.
Albion should really have made their bright start pay dividends on the half-hour after Greening picked out Kanu who in turn fed the ball to Ellington only for the former Wigan marksman to drag his shot wide.
It proved to be a costly miss as West Ham finally came to life. Reo-Coker was inches away from breaking the deadlock in the 41st minute when his curling free-kick slipped just past the post.
But he only had to wait another 60 seconds to break the deadlock although his smartly taken strike owed everything to the power of Bobby Zamora.
Zamora powered past the challenge of central defender Steve Watson and cut into the area. He looked to have overrun the ball only to see the alert Reo-Coker steer home a neat finish from ten yards for his fifth goal of the season.
United were then content to sit back on their lead and that was the signal for Albion to lay siege to their goal in the second half but without seriously troubling goalkeeper Shaka Hislop.
Ellington blazed over the bar after more good work by Kanu. Nigerian international Kanu, who had two penalty appeals turned down by referee Graham Poll, was then inches away from converting a Greening cross.
Nigel Quashie drilled a low shot wide and Curtis Davies saw his header deflected over the bar. Ellington then failed to hit the target from a pin-point cross by Greening as Albion endured a 90 minutes that perfectly summed up their season.