You need to get the first column with awk (You don't actually need this, but I'm leaving it as a monument to my eternal shame)
awk {'print $1'}
and then use awk again to sum the column of numbers and print the result
awk '{ sum+=$1} END {print sum}'
All together:
netstat -natp | grep 7143 | grep EST | awk -F' ' '{print $5}' | awk -F: '{print $1}' | sort -nr | uniq -c | awk {'print $1'} | awk '{ sum+=$1} END {print sum}'
I know this doesn't use bc, but it gets the job done, so hopefully that's enough.