The CPI and CPI(M) also noted the BJP clinched power in Assam for the first time due to "absence of strong secular and democratic" alternative and but said "it needs to be seen how the communal" saffron outfit works in the "sensitive" state.
Both the Left parties said their impressive performance in Kerala was "historic" yet "expected".
Accepting the people's verdict of returning J Jayayalalithaa's AIADMK to power in Tamil Nadu, the two Left parties alleged that money power played a crucial role the the southern states to ensure the victory for AIADMK.
"We respect the verdict of the people with all the humility in Bengal. We will examine and review the results in in order to draw proper lessons from it. We though salute our comrades, who worked unitedly despite the attacks by TMC," CPI(M) general secretary Sitaram Yechury told reporters here.
Yechury observed the BJP could open its account in Kerala due to vote transfer between the saffron party and Congress.
"Similarly, in West Bengal, the BJP benefited due to its match fixing with TMC," Yechury said. He though noted the BJP's voting percentage during the polls shown decline vis-a-vis its 2014 Lok Sabha election performance.
But at the same time he alleged that a reign of terror was unleashed on Left cadres in West Bengal. "There is no other go. We have to face it. Left cadres stood up to face it, to combat it. Had they not stood up, the results would have been different," he told a press conference.
Yechury claimed that 200 of Left cadres have been killed in West Bengal in the five year rule of Trinamool Congress. "We could not reach out to the people due to this," he claimed.
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Karat said the party's Kerala unit will meet tomorrow and hold discussions on who will be the next chief minister of the state.
Party veteran V S Achuthanandan and politburo member Pinarayi Vijayan, both of whom have won, are in the race for the CM's post.
On asked whether the CPI(M) leaders were taken aback by the party's poor show in West Bengal, its erstwhile bastion, Yechury stated the Left party had hoped to do better and therefore the results have come across as "setback" and said reasons for the same will be reviewed.
When queried about reports that daggers are out against him within CPI(M) over the West Bengal results, Yechury said that "all the decisions were taken by the party collectively".
"... It is your (of reporters) right to interpret it in the way you want to. But the responsibility (for the defeat in West Bengal polls) will be decided during review. As far we see, these are all decisions taken by party collectively and they will be reviewed," he said.
"Clearly, BJP was able to win some seats ably assisted by a vote transfer between BJP and the TMC. In Kerala, it could open its account due to similar assistance from Congress-led UDF there. It would not have benefited otherwise," he added.
Yechury also thanked party cadre from the state for fighting in an united manner against the "terror unleashed" by ruling TMC during and after polls.
In Tamil Nadu, the Parliamentarian said the People's Welfare Front (PWF), of which the CPI(M) was part of along with CPI, DMDK, MDMK, VCK and others - was "squeezed out" in the bipolar contest with the AIADMK and DMK, which he accused, used "money for votes".
"The PWF though will continue to work for interest of people in Tamil Nadu," he said. Yechury expressed satisfaction over first-time victory of a CPI(M)-supported independent candidate in the Puducherry polls.
Meanwhile, CPI national secretary too noted that the Left Front's impressive performance in Kerala was on "expected" lines, but underscored that communist parties need to do "serious introspection" about their strategy in West Bengal where TMC is set to retain power.