No, you can use the SQLite3 class to do it.
First, check that you've reloaded Apache after installing:
Then you can test it with the following code, which you can put in /var/www/test-sqlite.php (or whatever you like) and then run it in your browser.
sudo service apache2 reload
Check your /var/www/apache2/error.log for errors, and check that apache has permissions to write to the directory where it will create the DB file. This problem should be obvious from the logs.
// open the db file (test.db) if it exists, or create it if it doesn't
$db = new SQLite3('test.db');
// create a new table in the file
$db->exec('CREATE TABLE test (id INT, message STRING)');
// insert some things into it.
$db->exec("INSERT INTO test (id, message) VALUES ('1', 'test message')");
$db->exec("INSERT INTO test (id, message) VALUES ('2', 'test message 2')");
// make a select
$results = $db->query("SELECT * FROM test WHERE ID = 2");
// print some results