In-band crosstalk, due to multiple interferers, has been identified as one of the most severe impairments in optical transparent networks, especially in the ones with a large number of nodes and a high wavelength density. Due to its robustness to in band crosstalk differential phase-shift keying (DPSK) emerges as an attractive modulation scheme to be used in such environments. This paper proposes a rigorous formulation to estimate the performance of direct-detection DPSK receivers using an eigenfunction expansion technique in the time domain. The method takes into account both the in-band crosstalk, due to an arbitrary number of interfering terms, and the amplified spontaneous emission noise and is able to deal with any combination of optical and electrical filter shapes. Using this method the accuracy of an approximation based on the wide band optical filtering assumption was evaluated and shown that the approximation, although not providing reliable results for the error probabilities, can be used with confidence to compute power penalties due to in-band crosstalk. Furthermore, the crosstalk tolerance of DPSK over on-off keying was quantified and shown that this tolerance is reduced when the number of interferers increases.