Ten anti-strike craft cruisers is completely insufficient after the early game.
You have two options to deal with strike craft. The first is the obvious and shoot down the craft themselves, the second is to go after the carriers and blast them. Most players use some combination of these two approaches, but either way you're going to need lots of firepower.
To take out strike craft, you need lots of firepower in the form of fighters and flaks. You want to absolutely crush the enemy, and that usually means a large formation of flaks that shred any strike craft that fly overhead complemented by a large group of fighters to rip bombers apart. To take out carriers, you need frigate power, and for Vasari that usually means Kanrak Assailants and lots of them (Enforcers and Skirmishers also work well here, but Assailants offer you the best overall package). Now, most strategies will use a combination of these approaches, using flaks and fighters to thin out the enemy strike craft while the frigates rip through the enemy, but the exact balance and approach is really up to you.
Now, as mentioned, a Kortul Devastator capital ship with the "jam weapons" ability is highly useful here regardless of your approach, and for very large fleet battles (~50 or more enemy squads) it's a no-brainer.
