The 26-year-old was introduced from the bench by Hammers boss Sam Allardyce with 23 minutes remaining at the Madejski Stadium as the visitors chased an equaliser to Pavel Pogrebnyak's fifth-minute strike.
But Vaz Te, who was making his first appearance since dislocating a shoulder against Arsenal on October 6, will remember his comeback for all the wrong reasons after heading Matt Jarvis' cross wide of the post from just four yards out.
"I felt like I should have done better and I should have scored, there was no excuse for that," he told West Ham TV.
"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."
Allardyce saw defender James Collins gift Pogrebnyak the only goal of the game with a weak back-pass and bemoaned both the mistake from the Wales defender and Vaz Te's miss.
The 58-year-old said Vaz Te's late chance was one of the easiest in the history of the Premier League and the player agreed with him
"It was a great chance - the easiest chance I will ever have to score and I should have put it in the back of the net," said Vaz Te.
"I'm obviously very disappointed so I'm going to strive to do better next time. I'm going to keep work and keep improving and as my fitness picks up, I will surely do better."
Vaz Te's return to fitness comes at a time when West Ham are struggling with injuries but the Portuguese does not feel ready to play a full 90 minutes just yet.
"I'm not sure I am ready to start yet," he said. "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."