Where have you looked - Google have 20,700 references to Moncarapacho just on UK based sites!

Moncarapacho is not much more than a village a short way from Olhão. The next town in the other direction is Tavira which is well documented.

Fuseta would be the closest beach but like most in the area it is on a sand island and is reached by a short boat trip. If you don't fancy that it's not too far to Praia do Barril (near Pedras d'el Rei) which is also on an island but connected by a bridge you can walk over.

We have stayed in Fuseta and it is a lovely village.
As Steve says, the main beach is accessed by the little boat....BUT.... there is plenty of sand and sea on the town side if you don't want to go over to the main beach. Most of the Portuguese just stayed there and didn't bother to cross.
Pat

It's 5km/3.12 miles from Moncarapacho to Fuseta. I walked it once! There is a nice little beach on the landward side in Fuseta as people have said.