Buxton, who play in the Northern Premier League Premier Division, were the lowest-ranked team remaining in the competition.
Robinson said: “It was a real professional performance. Everything was massively set up for an FA Cup upset with the conditions and the surface, everything that went with it.
“The people watching on television were not watching to see Morecambe play nice football, they wanted a shock.
“We controlled a lot of it in horrendous conditions, and although we should have won by a lot more goals, it was job done.
“The be-all and end-all today was to make sure we’re in the next round and we did that.”
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