The find command combined with -exec or xargs can make this really easy.
If you want to execute psql once per file, you can use the exec command like this
find . -iname "*.sql" -exec psql -U username -d databasename -q -f {} \;
-exec will execute the command once per result.
The psql command allows you to specify multiple files by calling each file with a new -f argument. e.g. you could build a command such as
psql -U username -d databasename -q -f file1 -f file2
This can be accomplished by piping the result of the find to an xargs command once to format the files with the -f argument and then again to execute the command itself.
find . -iname "*.sql" | xargs printf -- ' -f %s' | xargs -t psql -U username -d databasename -q