This paper presents an analysis of phase errors generated by advanced noise removal algorithms applied to phase measurements obtained from digital holographic interferometry. The output phase error is analyzed considering two contributions: the error generated by the denoising method and the error due to phase noise. In addition, a third type of error allows quantifying the ability of any algorithm to estimate the initial noise level. A comparison of several denoising algorithms is presented to independently assess the three types of errors from a data set of simulated fringe patterns with controlled realistic noise. The results exhibit the best method for which the output error, together with the method error, is the smallest one. Knowing the error method is advantageously applied to digital color holography experiments in which deformation measurements of an object submitted to mechanical strength are given with a percentage of error due to the denoising algorithm.