Taxonomic clasification of BLAST output
This is basically metagenomics.
Congratulations, you already did the most time consuming step. 
There are several ways to go from there, but I will talk about the one I know best.
There is the metagenomic analysis tool MEGAN. It can read your Blast Output, if it is in the correct format (normal XML or tabular) and will automatically do what you want. 
For a start, just use the default values, for more help you an then go to the Community Website of MEGAN for help.

Analysing your data may take a little, depending on how many contigs you have. But if you were able to blast them in reasonable time it should be no problem. As I said, you are through the most time consuming step already.