The adsorption properties of different Carbon allotropes (i.e., graphene, γ-graphyne, Mobius graphene, and R-graphyne) and their corresponding Boron (N) and Nitrogen (N) incorporated BCN nanostructures toward carbon monoxide (CO) gas are studied via density functional theory calculation. All the adsorbents demonstrated negative formation energies and real frequencies, i.e., can be synthesized and have dynamical stability. The adsorption energies have increased due to B and N incorporation, although still comparatively low for practical application. The highest adsorption energy with suitable recovery time is observed for the Mobius BCN structure, about −0.112 eV and 77.8 ps, respectively. Very nominal charge transfer is observed via Mulliken charge distribution and electrostatic potential map analysis. The changes in energy gap and electrical conductivity are observed due to CO adsorption.