Forest begin the brightly by dominating the Premier League side but failed to make it count on the scoresheet.
Sabri Lamouchi’s were deserving of a goal and they finally got one in the 32nd minute, following some encouraging play.
Joe Lolley lifted a fine pass over the top of the Palace defence for Lewis Grabban, who got a toe to the ball to flick it towards goal, only for goalkeeper Wayne Hennessey to save as he rushed off his line.
But the keeper was helpless as Adomah pounced on the loose ball to drive a composed finish beyond him and inside the near post.
Adomah was replaced by compatriot Arvin Appiah in the 63rd minute of the game.
Adomah has joined Nottingham Forest in the ongoing summer transfer window on a two-year-deal after the winger was released by Aston Villa following their promotion to the Premier League.
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