Cole Stockton’s 29th minute goal was enough to ease the Shrimps into the third round hat at the expense of the plucky minnows.
The League One outfit had come under heavy pressure in the opening 15 minutes as the Bucks made the heavy wind in their favour count.
“It was a very professional performance,” said Robinson. The weather took away any advantage we had, I don’t think we have ever played in conditions as bad as that.
“We missed a lot of chances to make the game safe in the second half, but we are pleased to get through.
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“The object before the game was just to get through, it didn’t matter how.
“Everyone expected us to win. If we don’t it’s a disaster but if we win no-one says anything.
“Credit to Buxton, they pushed us. It was not easy today and the lads showed character.“We wanted to keep moving the ball and we knew they would tire and we would get our chances.
“It was all set up for a cup shock and credit to our players. A big Premier League side would be huge for us.
“We are still trying establish ourselves as a League One infrastructure and the finances would be massive.
“We are three years ahead of where we thought we would be and this would help us keep growing the club.”
Theo Richardson made a brilliant double save to deny Wesley McDonald and Stockton just before half-time as Buxton clung in there.
Wes McDonald, Stockton and Jonah Ayunga all wasted good second half chances for the visitors as the non-leaguers were just unable to find an equaliser.