The Culture Secretary added the Government will work “closely” with the Independent Press Standards Organisation (Ipso), the self-regulatory body, to ensure its “important work continues”.
Former Labour leader Ed Miliband led moves to amend the Data Protection Bill to establish a statutory inquiry dubbed Leveson part two.
But this was rejected by 304 votes to 295, majority nine, when pushed to a vote in the Commons - prompting cries of “shame” in the chamber.
Five Conservative MPs rebelled to support the measure, including former ministers Ken Clarke, Dominic Grieve and Crispin Blunt, while Labour’s John Grogan rebelled to oppose the amendment.
Ahead of the vote, Mr Hancock confirmed that Her Majesty’s Inspectorate of Constabulary would be undertaking a review of how police forces were adhering to new media relations guidance - as recommended by Sir Brian Leveson.
He added a person would also be responsible for reviewing standards of the press in Northern Ireland, which DUP MP Ian Paisley suggested could be viewed as a “Leveson for Northern Ireland” - an announcement branded “extraordinary” by Mr Miliband.
A separate Labour bid to introduce a measure forcing publishers not signed up to a state-backed regulator to pay their opponent’s legal costs in relation to alleged data breaches even if they won the case also faltered.
The SNP’s Brendan O’Hara said his party could not support a “system of press regulation that will be imposed from Westminster on Holyrood” and the amendments later fell after they were not moved to a vote.
Mr Hancock had warned such proposals would have had a “catastrophic” impact on local newspapers and risked making it “near impossible” to uncover stories of abuse.
Reacting to the vote on Leveson part two, Mr Hancock wrote on Twitter: “A great day for a free and fair press.”
But Mr Miliband tweeted: “Very disappointed for the victims of phone-hacking and press abuse that we did not win the vote for Leveson 2.
“The battle goes on to keep our promise to them to get the truth they deserve and protection for victims in the future.”
Society of Editors executive director Ian Murray welcomed the result, saying: “I am delighted that common sense has prevailed and the attempt to impose appalling penalties on the UK’s free press for failing to join a state-recognised regulator has been defeated.
“The defeat of proposals for a costly second inquiry into the press is also to be welcomed. As MPs heard, the press has already taken great steps since the Leveson Inquiry to meet the objectives of that report.”
Shadow culture secretary Tom Watson claimed there had been a “shameless capitulation to press barons” from the Tories which left victims of phone hacking “ever further from reaching the truth”.
He said: “No criminal investigation or trial has ever looked at the core questions that Leveson two posed: how the relationship between the press, police and politicians allowed the hacking scandal to happen and attempt to cover it up.
“Today was a chance for MPs to finally deliver on promises made to victims of hacking and press intrusion. That chance has been squandered and victims have been betrayed once again.”
Mr Watson later told MPs that the Bill had been a “missed opportunity”.
He said: “We consider this unfinished business and I have to say to the Secretary of State when he is in the twilight of his political career, as careers in this place always do end eventually, I feel he will come to
regret his decision to so stridently side with the press barons against those victims.”
Mr Watson added: “This Bill is necessary but there have been missed opportunities, a missed opportunity to correct the sins of the past on Leveson but also a failure to look at how we begin to look at the future of data capitalism and its impact on people in the new digital age.”
The Bill received its third reading unopposed and will return to the House of Lords at a future date for further scrutiny.