Lucas Paqueta fired the Hammers ahead in the third minute, only for goals from Taiwo Awoniyi and Anthony Elanga either side of the break to put Forest into the lead.
But headers from Jarrod Bowen and Tomas Soucek, both from James Ward-Prowse corners, allowed Hammers to claim a first Premier League victory since September.
“Yeah, I needed that. But so do all the clubs,” said Moyes, having seen his side beat Olympiacos in the Europa League on Thursday evening.
“I was thrilled with the opening minutes, and with the end few minutes. But our play was too slow in the first half and we lost a goal before half-time as well.
“In the second half, after we went behind we played really well to get ourselves back in the game and to win it was tremendous. ”
Ward-Prowse has now contributed nine assists in all competitions since joining West Ham from Southampton, yet an England call-up still eludes him.
“I’m quite pleased that he’ll get a rest this week, with the amount of games we’ve had,” added Moyes with a smile.
“Let’s be fair, he is world-class at his deliveries, and if I was him I’d be disappointed the other boys haven’t scored more from his deliveries.”
Steve Cooper felt Nottingham Forest threw away the chance of a rare away win in east London.
Forest have won just two matches on the road since they were promoted in 2022.
“I think if we’d drawn 2-2, I’d have been disappointed,” said Cooper.
“I can’t look past the goals we’ve given away. We gifted them a goal at the start, worked our way back into it and then to concede a corner after five seconds from kick-off and defend like we did is frustrating.
“The third goal is from our throw-in, it’s a corner again and we didn’t do our jobs. Whether the ball coming in is brilliant or average, you’ve got the stay with your man.
“We know we are doing a lot better things away from home but we’ve just thrown a result a way, and to lose it like we did, it was our own fault, I can’t look past that,” Cooper added.
“There was a real opportunity to come here to win and we were doing that. Today was a different away performance and loss.
“This is one we are going ‘We’ve just thrown it away’. This could have been a much more comfortable day and we’ve only got ourselves to blame.”
*copy from Press Association.
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