The Premier League side, drawing 1-1 from the first leg at the London Stadium last week, deservedly triumphed 3-0 at the Groupama Stadium on Thursday night to knock Lyon out of the competition.
And Hammers midfielder Rice insisted Lyon's gloating and taunting "came back to bite them" and was an incentive for the visiting team.
He said: "Obviously (Moussa) Dembele winking at the camera in the first leg and then their Twitter admin somehow saying they don't know how they're not going to get through.
"So those things come back to bite you and we stayed quiet, put in a performance and now West Ham are in the semis.
"What more do we want?"
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