'Gutted' Moyes laments Manchester City winner
West Ham remain second bottom of the Premier League but were good value for their half-time lead against City, with Angelo Ogbonna heading home Aaron Cresswell's cross.
Pep Guardiola's league leaders improved after the break and Nicolas Otamendi's close-range equaliser came amid mounting pressure.
The 83rd-minute winner came when David Silva launched himself to acrobatically turn in Kevin De Bruyne's brilliant chipped pass but Moyes pointed towards something of a learning experience for 18-year-old Rice, who he credited with impressing up until that point on his third top-flight start.
"I think we should have done much better with it," the former Everton and Manchester United boss told Sky Sports.
"I'd have thought if you're a centre-half dealing with that you'd head it away.
"But you've got to remember we're playing a young 18-year-old centre-half who played really well.
"They've shown heart and character but I've seen that in training every day. They're a really good group of boys and they're working hard to get away from trouble.
"Against the top teams you've got to do it for 90 minutes, not 70 or 80 and we've got some other big games coming up."
144 - Angelo Ogbonna's goal was his first ever in one of the big five European leagues, in what is his 144th appearance. Shocked. pic.twitter.com/oNlxWcgrFV
— OptaJoe (@OptaJoe) December 3, 2017
Chelsea and Arsenal are up next in back-to-back home games at London Stadium but Moyes can take heart from a vast improvement upon Wednesday's 4-0 thrashing at Everton.
Michail Antonio and Manuel Lanzini might have already capitalised on a lethargic opening half from City before Ogbonna did so.
"We're gutted that we lost it," Moyes said. "We played against a really good side and I thought for long periods we frustrated them.
"Arguably we had the best chances in the first half.
"We're disappointed not to have taken anything from the game but we're really proud of the players.
"Eventually Manchester City will force you back. We weren't good enough at keeping the ball but the defensive set-up was brilliant.
"So many of their players can cause you problems but in the main our players did really well."