However, Moyes will try to take the positives with the East London outfit squandering numerous opportunities in front of goal against a Watford side who ended their run of three successive defeats.
Within the first 30 seconds of the game, Andy Carroll left Watford debutant Marvin Zeegelaar requiring treatment for a bloody nose, and it set the tone for a first half which saw four players given yellow cards.
However, the first and only chance of the opening quarter of the game led to a goal, with Hughes directing the ball into the bottom corner from eight yards after Andre Gray's scuffed shot had gone to the feet of the former England Under-21 international.
A clever through-ball to Kouyate left the midfielder with only Heurelho Gomes to beat from 10 yards out, but the Brazilian goalkeeper somehow diverted the ball behind for a corner.
Just before the half-time whistle Arnautovic had an even better chance after seeing his initial header parried, but Gomes managed to stick out a hand to claw the ball off the line.
Soon after the restart, West Ham created another opening which should have been taken after Arnautovic had done well to get to the byline, but Kouyate blazed over the crossbar from no more than 12 yards.
The midfielder's miss led to a period of sustained pressure from the home team, with Abdoulaye Doucoure curling just wide of the far post and Gray sending a deflected effort marginally off target.
Hart was also forced into a save from a point-blank header by Adrian Mariappa, but Watford eventually added a second through Richarlison, who ran towards goal from the left flank before sending a shot into the far corner of Hart's net.
To their credit, West Ham continued to press for the goal which their play in the final third had deserved, but the visitors again missed out when Mariappa cleared the ball off the line after Manuel Lanzini's well-struck effort had beaten Gomes.
That opportunity proved to be West Ham's last real chance and it became a case of whether Watford would add a third goal during the closing stages of the game.
Richarlison curled a late effort wide of Hart's post but Marco Silva will be content with just a second home win of the season and a first clean sheet in eight matches in the top flight.