The defeat leaves West Ham 18th in the Premier League table, and Noble acknowledged that the team has badly underperformed this season.
"It's a very difficult situation for us. The fans show their emotions, and rightly so because they're not happy and they pay a lot of money to come and watch us. I know it's hard, I know they're frustrated, and we are too because we know we're better than what we're showing, but I urge them to stick by us and hopefully the good times will come back," he told West Ham TV.
"As much as we're not performing on the pitch at the minute, we need them to stick by us. We had good chances to equalise in the first half but in the end I thought Watford were the better team.
"They have been together with their manager for a while and we've had a couple away on international duty and we've trained with our young lads. It could have been a different if we'd finished our chances but that's the way it's going at the moment. There's a bit of a lack of belief in our players and I think we showed it."
The Hammers have now picked up just two points from the last 15 on offer in the Premier League.