As @DoubleAA asserts if the crumbs are small, the bittul would suffice.
That aside, there is also the concept of “Yisrael Kedoshim Heim”, in other words since Jews are a holy people, there are those who take on to be extra stringent and try and eliminate even the smallest amount of chametz (e.g. see the Tur 442, Kaf HaChaim 442:69 etc.) (- Speak to your local Rov for guidance as to whether to apply these chumros or not.)
In such a scenario, a widespread practise is to spray cleaning fluid/bleach on the offending chametz, thereby rendering them inedible and therefore no longer an issue. It is the same principle as biur chametz, in that when the food becomes significantly spoiled it is no longer regarded as "food".
Note the following based on the writings of the Shulchan Aruch HaRav:
Chametz that is stuck in a deep hole or crevice and cannot be reached with one’s hands, is not required to be removed and it suffices for him to nullify the Chametz before Pesach. This applies even if there is a Kezayis of visible Chametz found in the crevice. Nonetheless, practically, the Jewish people are holy and destroy all Chametz that is in one’s possession, even if the Chametz found in unreachable areas. Thus, when possible, one is to pour bleach or other spoiling agent over Chametz that he is unable to reach with his hands.