The 27-year-old had his return to Stamford Bridge cut short after he was forced off in the 16th minute with what appeared to be a hamstring injury.
Dewsbury-Hall has impressed since joining Everton in the summer, scoring four goals and providing two assists in his 16 games across all competitions.
Speaking after the game, Everton boss Moyes admitted losing the midfielder was a ‘blow’ and that he doesn’t know how severe the injury is just yet.
“I’ll find out later what it is, he had a bit of tightness already and then he felt it during the game,” the manager told Sky Sports.
He later told BBC Match of the Day: “Losing Kiernan was a blow to us but I thought we adapted quite well.
“I know we’ve come away with a disappointing result but it wasn’t a disappointing performance. We did a lot of really good things today.”