Mr Hoon admitted his push for a secret ballot "is over".
Former minister Geoff Hoon could face a vote of no confidence from his constituency, following his call for a ballot on Gordon Brown's leadership.
Following a meeting of the Labour Party members in Ashfield, Nottinghamshire, Mr Hoon told the BBC he was not "carried aloft like a conquering hero".
He said while he faced criticism, he also had some supportive comments.
The BBC understands that some activists are considering tabling a motion of no confidence in him as their MP.
They think he had not apologised sufficiently tonight for his role in potentially destabilising Gordon Brown's leadership of the Labour Party, in the run-up to the forthcoming general election.
Mr Hoon told Friday night's meeting he was remaining as the candidate for the next election.
Earlier, Ashfield District Council leader John Knight said activists were "shocked and disappointed" at Mr Hoon's involvement in the challenge.
Mr Hoon replied that Labour "thrives on political debate" adding: "He's entitled to his view and I'm entitled to mine."
Earlier, he admitted his push for a secret ballot on Mr Brown's leadership "is over".
But he told the BBC he did not regret sending a letter to all Labour MPs calling for a vote on the issue.
On Wednesday, former Defence Secretary Mr Hoon and former health secretary Patricia Hewitt urged a secret ballot of Labour MPs on the Labour leadership, saying the party was "deeply divided" on the issue and it had to be sorted out "once and for all".
But only a handful of backbench MPs publicly supported the move and throughout the day cabinet ministers spoke against it.
Mr Brown has called it a "storm in a teacup" but there has been continued speculation about his level of support among cabinet colleagues.
The BBC's political editor Nick Robinson said, in the period before senior ministers publicly rejected the revolt, Mr Brown had a meeting with Justice Secretary Jack Straw and Commons leader Harriet Harman - who demanded a widening of his leadership circle - and with Chancellor Alistair Darling.
Mr Brown's spokesman said he had made no reference to the failed ballot on Friday morning at the cabinet meeting, the first since the news broke, instead telling ministers of the "importance of a laser focus on the key issues of the country" - such as the economy and severe weather.
Meanwhile, on the campaign for a ballot, Mr Hoon told the BBC: "I think it's probably over. I accept that we made that opportunity and we don't appear to have succeeded... We set it out and it's really for them [Labour MPs] to decide."