A recent study (Sci. Adv. 2017, 3, e1602833) has shown that FH⋅⋅⋅OH hydrogen bond in a HF⋅H O pair substantially shortens, and the H-F bond elongates upon encapsulation of the cluster in C fullerene. This has been attributed to compression of the HF⋅H O pair inside the cavity of C . Herein, we present theoretical evidence that the effect is not caused by a mere compression of the H O⋅HF pair, but it is related to a strong lone-pair-π (LP-π) bonding with the fullerene cage. To support this argument, a systematic electronic structure study of selected small molecules (HF, H O, and NH ) and their pairs enclosed in fullerene cages (C , C , and C ) has been performed. Bonding analysis revealed unique LP-π interactions with a charge-depletion character in the bonding region, unlike usual LP-π bonds. The LP-π interactions were found to be responsible for elongation of the H-F bond. Thus, the HF appears to be more acidic inside the cage. The shortening of the FH⋅⋅⋅OH contact in (HF⋅H O)@C originates from an increased acidity of the HF inside the fullerenes. Such trends were also observed in other studied systems.