I just tried to liquify some celery and broccoli, but I still have tiny chunks. Is there anything that I can do other than straining or using a blender?
The blender is probably the best alternative. Food processors are not made to juice fruit or vegetables--they don't remove the pulp from the liquid.
A Vita-Mix is the best and it lasts for decades. I make green drinks all the time. Blenders don't have the power.
Some things will be beyond a food processor's ability. But if you are liquifying vegetables it would help if it is fully cooked, and a little additional liquid is added in. You will also need to run the processor a lot longer. Once again some vegetables will be beyond a processor's ability. Hope this helps.