The Pivot Table will always pull the unfiltered data for its source.
You can cheat a bit by creating a Table from your Source sheet. Then as you add columns to your Pivot, they should bring the Table filtering that you've already done with them.
Also, you can then filter the data directly in the Pivot Table. Depending upon your data source, you could pre-filter the data before it gets to Excel. I do this fequently using SQL as a data source and writing a view that pre-filters data before importing.