The party also said the results of West Bengal and Kerala will be a disappointment for the "Left and democratic forces" but this will not make the Left policies and programmes "irrelevant" for the country.
'Paribortan' or change -- the poll plank of Trinamool -- found an echo in the words of senior CPI-M leaders Sitaram Yechury and Brinda Karat as well as a party politburo statement which said the party accepts the people's verdict.
"After the Left Front being in office for a record 34 years continuously, the people have opted for a change. The TMC-led combine has been the beneficiary of this change," the CPM statement said.
"Vahan pe janta mein parivartan ka aasha rahi (People had hoped for a change there)," Yechury told reporters.
Karat said the issue of land acquisition in Singur and Nandigram had created a perception that the government is going against its own land reforms programme, which was, however, "not its intention". She said there are questions of whether the situation was "mishandled".
"But we are confident that we will get over the mistakes and regain the confidence of people of Bengal," she said.
As Banerjee's party rode an anti-Left wave, the party said it will analyse the results carefully at a politburo meeting on May 16 and come to proper conclusions about the electoral reverse.
It said there were solid achievements during the Left rule including land reforms, a democratised panchayat system, progress in agriculture, assurance of democratic rights for the working people, for unity, integrity and communal harmony.
"These are historic gains of the people of West Bengal and an enduring legacy," it said.
The party also appealed for peace following the verdict, saying, "There should be no repetition of the violence that took place against the CPI-M and the Left Front cadres and offices in the aftermath of the Lok Sabha polls in 2009."
The party said the election results in Kerala show that the people have by and large endorsed the record of the LDF government of the past five years.
"The Left Democratic Front has very narrowly lost the elections with the UDF getting a slender majority of only two seats. This shows that there has been no anti-incumbency trend. However, some caste and religious forces have worked to influence the elections," it said.
It termed the Tamil Nadu results as a decisive rejection of "corrupt misrule" of the Dravida Munnetra Kazhagam and a "verdict against the corruption which has flourished under the United Progressive Alliance regime" at the Centre.
Yechury said the peace talks with the United Liberation Front of Asom and the division in the opposition parties have contributed to the Congress's gains in Assam.