To investigate the effects the cluster environment has on late-type galaxies (LTGs), we studied HI perturbation signatures for all Abell 1367 LTGs with HI detections. We used new Very Large Array HI observations combined with AGES single-dish blind survey data. Our study indicates that the asymmetry between the high- and low-velocity wings of the characteristic double-horn-integrated HI spectrum as measured by the asymmetry parameter, Aflux, can be a useful diagnostic for ongoing and/or recent HI stripping. 26 per cent of A1367 LTGs have an Aflux ratio, more asymmetrical than 3 times the 1s spread in the Aflux ratio distribution of an undisturbed sample of isolated galaxies (2 per cent) and samples from other denser environments (10 per cent-20 per cent). Over half of the A1367 LTGs, which are members of groups or pairs, have an Aflux ratio larger than twice the 1σ spread found in the isolated sample. This suggests intergroup/pair interactions could be making a significant contribution to the LTGs displaying such Aflux ratios. The study also demonstrates that the definition of the HI offset from the optical centre of LTGs is resolution dependent, suggesting that unresolved AGES HI offsets that are significantly larger than the pointing uncertainties (> 2σ), reflect interactions which have asymmetrically displaced, significant masses of lower density HI, while having minimal impact on the location of the highest density HI in resolved maps. The distribution of Aflux from a comparable sample of Virgo galaxies provides a clear indication that the frequency of HI profile perturbations is lower than in A1367.