You may be quite adept at squirting paste dewormer into your horse's mouth. But even with the best technique you won't succeed in delivering the medication if you don't make sure his mouth is empty first.
A least 10 minutes before you administer dewormer, restrict your horse's access to forage or grain. That way, he won't have a partially chewed wad in his mouth to get in the way of the dewormer or to aid his efforts to spit it out.
Either remove his hay and grain or tie him so he can't reach them. If you suspect he's still concealing a last bite, carefully open his mouth by placing your fingers in the toothless bars, as you would if you were inserting a bit. A little thumb pressure against his tongue will encourage him to swallow. If necessary, use a catheter-tip syringe to flush his mouth with water.
When you're sure that your horse's mouth is empty, deliver the medication and watch for a moment or two to verify that it doesn't come back out. Dewormers are formulated to be extra sticky and cling to the roof of the mouth, so it's unlikely any will escape.