The Hammers were 2-0 ahead at the break at Stamford Bridge, which saw Chelsea's players booed off by the home support.
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In response, Sanchez was seen shouting at jeering fans, the Spain international told Blues supporters: “Support your side.
“We got 45 minutes to go, it is never done.”
In the end, Sanchez was proven right as Chelsea fought back to win 3-2, as Enzo Fernandez struck the hosts' third goal in injury-time.
The win sees Chelsea sitting in fifth place on the Premier League table, one point outside the top four.
Watch below: