Ukip leader Nigel Farage conceded his party had been defeated during the by-election, but hailed the result as Ukip's "strongest ever by-election performance".
Speaking after the result, Mr Farage said: "I think there'll be an awful lot of Conservatives with a majority of less than 10,000 who will look upon this result in sheer horror."
But he admitted he would have liked to have done better in Newark.
"Yes, I mean the majority's halved, but nonetheless for Ukip it's still a good night's work," he said.
David Cameron has hailed the Newark by-election result as "very good for the Conservative Party" but he said the Tories needed to "work between now and the next election" to win back voters from Ukip, who came out second in the by-election.
The PM was speaking in Bayeux, France ahead of D-Day commemoration events.
Asked how he would win back support from Nigel Farage's party he acknowledged the challenge posed by Ukip:
"The job isn't finished yet but we are on the right track, let's stick at it."
Prime Minister David Cameron has hailed the new Conservative MP of Newark, Robert Jenrick on Twitter by saying he will work to deliver a "brighter future".
In @robertjenrick the people of Newark will have an MP who will fight for them and work to deliver a brighter future for all.
The new Newark MP has dismissed the success of UKIP, saying his party fought a campaign on local issues. Conservative Robert Jenrick replaces the former MP, Patrick Mercer, who stepped down over a "cash for questions" row.
UKIP made big gains to come second in yesterday's by-election. The Tories' majority was cut significantly from over 16,000 to just over 7,000.
After the Conservatives win in the Newark by-election, Labour candidate Michael Payne has revealed he will push Robert Jenrick all the way "to the General Election."
Robert Jenrick, the Conservative candidate, won the Newark by-election with Ukip coming in second and Labour in third.
Speaking this morning, Labour's candidate spoke of how proud he was of his party's campaign during the by-election.
He said: "While this was always going to be a tough by-election, I am extremely proud of the campaign that Labour has fought.
"In the months ahead, I'll continue campaigning on those issues and holding Robert Jenrick to account right the way through to the General Election."
The Conservative's Robert Jenrick has won the Newark by-election with a majority of over 7,000.
Other candidates scored the following votes:
Nick the Flying Brick (The Official Monster Raving Loony Party) - 168
Andy Hayes (Independent) - 117
David Bishop (Bus-Pass Elvis Party) - 87
Dick Rogers (Stop Commercial Banks Owning Britain's Money) - 64
Lee Woods (Patriotic Socialist Party) - 18
The Conservative Party has held the Newark seat vacated by Patrick Mercer.
Robert Jenrick has taken the seat with 17,431 votes.