A 4th minute headed goal from defender Ronnie Fletcher appeared to set the Hammers on their way to a deserved victory, but a host of missed chances gave Forest a lifeline and they snatched an equaliser midway through the second half.
Breaking away on the counter-attack, a cross from the right was missed by goalkeeper George Sealey, allowing the Forest striker to head home in the six yard box.
By then, though, the game should have been sewn up by Peter Brabrook's team, with Greg Pearson, Mitchell Cole and Craig Saunders all missing golden chances.
Said Peter: "In the end it was a real disappointment because we should have won the game convincingly.
"Once again, it was the problem of being unable to finish our chances that cost us. It has troubled us all season and I've been saying all year that a team is going to take a hiding from us soon - but it hasn't happened yet!
"We should really have been 3-0 up at half-time and then scored a couple more in the second half, but we just didn't take our chances.
"Forest's goal was disappointing from our point of view. George Sealey missed the cross and the smallest player on the pitch headed it in."
In the other game in Hammers' play-off group, Arsenal beat Everton 2-1, meaning that Brabrook's team must beat the Toffeemen next week to stand any chance of progressing to the knockout stages.
Team: Sealey, Lumsden, Tattum, Saunders (Noble 85), Ward, Fletcher, Collington (Morris 74), Ferdinand, Akinsete, Pearson, Cole. Subs unused: Parrington, Laws, McClenahan.
*The under-19s match against Reading was postponed due to a waterlogged pitch.