Influential centre-back Reid was replaced by Declan Rice shortly before Ashley Williams headed home Everton's final goal in a harrowing 4-0 defeat for the Hammers on Wednesday night after appearing to suffer a hamstring injury.
Carroll was a surprise omission from West Ham's matchday squad at Goodison Park, with Moyes revealing before-kick off that the injury-prone striker sustained a knee problem during training on Tuesday.
"He just went over on his knee yesterday," he told BT Sport. "Rocked his knee in training yesterday so unfortunately, he's not available tonight.
"It happens doesn't it? Clubs get injuries and you get that. It can happen."
Those two setbacks pile yet more misery on an already beleaguered Moyes, who welcomed back Michail Antonio against former club Everton but was still without Javier Hernandez, Jose Fonte, James Collins and Sam Byram. Marko Arnautovic featured for 62 minutes on Merseyside despite limping out of last week's 1-1 draw with Leicester City.
Such a heavy loss to a fellow struggling team playing their final game before Sam Allardyce replaces caretaker boss David Unsworth left West Ham mired in the relegation zone, still two points adrift of safety ahead of a tough stretch of games that includes successive contests against unbeaten City, Chelsea and Arsenal.
Moyes claimed he witnessed a drastic improvement after a wretched opening 45 that saw the visitors trail 2-0 at the interval and believes the final scoreline was harsh on his side, who could have pulled back within one goal had Jordan Pickford not saved Manuel Lanzini's penalty before Wayne Rooney completed his hat-trick with an incredible finish from inside his own half.
"Not good in the first half but a massive improvement at half-time," he told BBC Sport. "We didn't deserve that final score. Mistakes cost us. The missed penalty was the turning point. It looked too difficult a challenge once we didn't score it. We never really got at it from the start. We allowed them to get a bit of confidence.
"The penalty changes it, it's poor defending from us. Their goals were too easy to score. Joe [Hart] kicks it and Wayne scores from the halfway line. We made our own mistakes. We want to set the team up to be hard to beat and that wasn't difficult tonight.
"It's what Wayne can do. He's always got goals in him and technical ability. He's got the knack of being in the right place to score goals. I think we saw some positive signs in the second half. It didn't go for us when we needed it. There were a lot of small things we needed to go for us."