Hernandez emerged from the bench to attain an important equaliser within the 1-1 draw at Chelsea on Sunday.
Evra, meanwhile, replaced the injured Aaron Cresswell in the second half and looked solid on his first appearance in over a month.
"We came out here today with a a point and that's massive for us going into the last six games of the season", Rice added.
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Cesar Azpilicueta had given Chelsea the lead on 36 minutes after getting on the end of Alvaro Morata's knock-down, but Javier Hernandez levelled for West Ham following the break to earn the Hammers a precious point. I'd watched clips and obviously I know how Eden Hazard plays and how Willian plays, but you can't really tell off a video until you face them in real life as you come up against different challenges.
"Joe Hart probably needed a game like that".
The teenager, who again played as one of three centre-halves, admitted he had tried to bone up on Antonio Conte's men as much as he could in advance but that he learned most on the job. "But I think this game describes very clearly our season".More news: Celtics routed by Raptors
"It was a good weekend for us because they were singing my name, then I scored and I could celebrate with them".
But rather than discuss whether his team should have had a penalty that may have won them the match, Moyes instead insisted he would rather talk about West Ham's positive display. How many times have I said that we didn't take the chances we created? "About what? I like to continue to say "we need to continue to work and improve", but you must win this game if you want to reach a target", the Italian replied when asked about finishing in the top four. "I thought I saw a definite movement with his knee towards Jack".More news: CWG 2018: Weightlifting gold rush continues, Punam Yadav claims 5th for India
But next Monday they host fellow strugglers Stoke knowing a defeat would drag them right back into trouble ahead of a tricky run-in including fixtures against Arsenal, Manchester United and Manchester City.
West Ham team: Hart, Ogbonna, Cresswell, Rice, Noble, Zabaleta, Kouyate, Masuaku, Arnautovic, Joao Mario, Fernandes.More news: Buses in Syria's Eastern Ghouta for more evacuations
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