Rithika Kumar and Swapnil Bhandari of IDFC Institute, demystify the reasons for DMK's loss in the Tamil Nadu assembly elections in this Firstpost article. Contrary to what is claimed by M. Karunanidhi, the election loss can be attributed to an alliance math that went wrong. Kumar and Bhandari write:

"To put things in perspective, this election was a game changer for two reasons. One, J Jayalalithaa created history by getting re-elected in a state that, since 1984, has never seen an incumbent return to power. Two, since Tamil Nadu elections are usually one-sided affairs with either the ADMK or DMK toppling the other, DMK's performance was exceptional for an opposition party. In light of this, our analysis uses constituency-level data to glean insights on DMK's performance. Having fallen out with former allies like Desiya Murpokku Dravida Kazhagam (DMDK) and the Left after the 2011 election, AIDMK went solo in 2016. The Congress tied up with its existing ally, DMK, contesting 41 seats, down from 63 in the previous election. With the BJP contesting 187 constituencies, it became a six-cornered fight (including PMK and the Vijaykant-led Third Front), which turned out to be disastrous for all but the two regional giants."

You can read the full article here