The Scot was appointed by the struggling Premier League club at the beginning of November but began his reign with a loss at Vicarage Road.
"Most people would have expected something like that performance," Moyes told Sky Sports News. "I was disappointed we didn't do better, but we missed some really big chances.
"The better team won the game, but there was a chance to change the outcome of the game. We have to improve.
"I was only ever going to find out what the players were like by working with them and seeing them play today. When the opportunities didn't go for us, the confidence went away.
"We have to try to find a way of winning. The important thing is to be in the game, and when we lost the second goal, it became difficult."
The result sees West Ham remain in the Premier League's bottom three with nine points from 12 games.