He spoke of his desire to “unleash” the Labour movement to win its first general election since 2005.
The left-wing MP, writing in the Guardian, said: “The truth is that while making a clear break with the New Labour era in terms of policy and personnel, the party was never able to communicate this to voters in our heartlands.
“When trying to persuade them of our radicalism and sincerity, we often had the legacy of the 2000s thrown back in our faces.
“Persuading voters that we understand the sources of their long-held resentment and frustration, of their disappointment in how Labour has conducted itself since the 1990s, will be the first step towards winning back their trust.”
Rachael Maskell, MP for York Central, has been quick out of the blocks to endorse Mr Lewis for leader.
The contest to succeed Mr Corbyn has yet to officially start but a number of other candidates are expected to declare in the coming weeks.
Emily Thornberry confirmed on Wednesday that she would also run in the race.
Shadow business secretary Rebecca Long-Bailey is said to be considering running, while shadow Brexit secretary Sir Keir Starmer, Wigan MP Lisa Nandy and arch-Remainer and Tottenham MP David Lammy have all expressed interest.
Ms Long-Bailey is seen as the contingency candidate, due to her close ties to Mr Corbyn.
Mr Corbyn announced he would not lead Labour into another election, following the party’s performance on December 12.
He has called for a period of reflection in the party and said he will remain in his position until a new leader is selected.