But after coming off the bench for just his second Premier League appearance in the
goalless draw at Newcastle at the weekend,
the midfielder will hope his goal can cement his place in manager Sam Allardyce's plans.
West Ham's Matthew Taylor and Cheltenham's Richards both went close with early free-kicks before Morrison, making his full debut along with goalkeeper
and Leo Chambers, was cautioned for diving in the area.
However, moments later Morrison was judged to have been fouled outside the box and Vaz Te put the Premier League side ahead with a bending free-kick.
Morrison doubled the advantage in the first minute after half-time when he made the space to score with a shot from just outside the area.
Richards pulled one back with a penalty on the hour mark after Adrian fouled Deering.
Byron Harrison and Robins captain Russell Penn came close to scoring for the League Two outfit, but the Hammers, who had Alou Diarra stretchered off in the first half, held on to progress to round three.
VIEW FROM THE DRESSING ROOM
Cheltenham manager Mark Yates told BBC Gloucestershire:
"Up until they scored a worldy free-kick they didn't hurt us.
"The second goal was a killer blow but we responded brilliantly, to be fair.
"We did well - probably the best we've done against the three Premier League teams we've faced.
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