As of now there simply isn't any other way.
Last year's compendium had a few ways of leveling up your compendium through daily hero challenges and what not.
The community has launched somewhat of an outcry towards Valve in hopes of having a few ways of leveling up your compendium that doesn't include spending more money.
Give it a few days and you might see more ways of increasing your compendium level.
Edit: 15/5 -15
Added a fourth Challenge, which is always a Hero specific Challenge, and rewards completion with both Compendium Coins & Points.
Challenges are now available in Captains Mode, Captains Draft, Random Draft, Single Draft, and All Random game modes.
Ten Hero Challenge added to compendium, also enabled on the above mentioned modes. This year you can do the Ten Hero challenge 3 times for a total of 450 Compendium Points (4.5 Levels).
You can now destroy an Immortal to gain 200 Compendium Points for each.
Added back the Item Recycling system. You can now recycle 10 items for a Charm of the Crucible Jewel II and 25 Compendium points.
Added 3 Recycle Charm Achievements. Create 1 Charm, Create 10 Charms, and Open 8 Charms. Worth 50, 125, and 200 points respectively.
Added All-Star match voting (provides 50 Compendium Points).