"We go into Monday's game with confidence high, but with the knowledge that we can not afford to let our levels of concentration or performance drop against a Stoke team who are fighting for their lives", Noble wrote in West Ham's Official Programme.
Peter Crouch climbed off the bench to take advantage of a Joe Hart error to put the visitors ahead before Andy Carroll struck late on to snatch victory away from the Potters.
"It is a blow because we were so close to winning", Lambert told Sky Sports.
"We didn't go out there with it really planned".
Moyes has stated that Rice, who can operate as a central defender or as a defensive midfielder, has shown a lot of maturity in his last two performances.
Former Stoke player Marko Arnautovic has been involved in 13 Premier League goals this season (nine goals, four assists), five more than any other West Ham player.
Meanwhile, Stoke are still desperately searching for their first win since Paul Lambert's victorious first game in charge.
"He's someone who needs the confidence, but I think he also needs the understanding of how you get to the levels you've got to". I couldn't ask for any more from my players.
They are one loss short of reaching 1,000 defeats in the top flight and would become the 16th club to reach this landmark. He was the one that showed us, and going to centre-forward freed him up a little bit. There were a lot of good things about about our performance.
"I don't think he will (slack off) now, because he knows what got the crowd from booing him to cheering him every week and becoming one of their heroes".