The French international started Sunday's Premier League fixture at Old Trafford, but sustained a heavy blow to the head following an accidental collision with team-mate Kurt Zouma.
Areola was then withdrawn at half-time, replaced by deputy Lukasz Fabianski as West Ham fell to a dispiriting 3-0 loss courtesy of Alejandro Garnacho's brace and another goal by Rasmus Hojlund, despite an impressive first-half performance.
However, it does not seem that the 30-year-old - who was also taken off late against Sheffield United a fortnight ago after a blow to the head - stands to miss any time, with Hammers boss Moyes confirming after the game that he was feeling okay and had been replaced as a purely precautionary measure.
West Ham face title-chasing Arsenal at home next weekend in a huge London derby.
"It was just a case of we were making sure we were not doing the wrong thing," Moyes told the BBC of Areola's substitution.
"He is fine, we just felt there was no point risking him."
Moyes felt a 3-0 defeat was harsh on his side, who had 13 shots in total in the first half alone but missed the creativity and production of the injured Lucas Paqueta.
"No I don't think the scoreline was correct," Moyes said. "Our performance in the main was much better.
"I am pleased with that but obviously not pleased with different aspects, we didn't finish chances. Overall we played better and our performance was better today."
The pivotal moment in the game for West Ham came shortly after half-time, when Emerson Palmieri was guilty of a terrible miss at one end before Garnacho's shot at the other deflected in off the unfortunate Nayef Aguerd less than a minute later.
"That tells you it just was not going to be our day," Moyes said of the Emerson miss. "They broke away and they shoot and it takes a big deflection and that makes it 2-0.
"We have been on a pretty good run without being at our best, with some players also away. I thought today we looked like it but goals have been a little hard to come by. Hopefully there's a wee bit of mitigating circumstances and hopefully the goals will start flowing in the coming weeks."