Pavel Pogrebnyak scored the only goal of the game for the Royals in the fifth minute but Vaz Te missed a glorious chance to equalise for the Hammers after being introduced from the bench with 23 minutes remaining.
The 26-year-old, who was making his first appearance since dislocating a shoulder against Arsenal on 6 October, headed Matt Jarvis' cross wide of the post from just four yards out when completely unmarked.
West Ham boss Sam Allardyce later labelled it "the easiest chance to score a goal you'll ever see in a Premier League football match".
"I felt like I should have done better and I should have scored, there was no excuse for that," Vaz Te told West Ham's website.
"I'm just very disappointed with the result, especially after coming on and having a great chance to score.
"I'm just really disappointed I couldn't make it for the lads. I felt like I let everybody down and I'm just going to try to do better next time.
"I'm going to keep working and keep improving and as my fitness picks up, I will surely do better.
"I'm not sure I am ready to start yet. I have only trained the past week and I didn't play any games before. I played for 20 minutes at Reading and it was quite hard, so I'm just going to keep training to get my fitness as quick as possible.
"I will do my best if the gaffer decides to put me on. Personally, I don't think I'm ready to start a game but if that's the gaffer's choice I will always do my best, like I said."