Deputy Prime Minister John Prescott, who announced that he would step down from his post over the next year, apologised to the party for an extra-marital affair he admitted to earlier this year.
"I know in the last year I let myself down - I let you down. So conference, I apologise," Prescott told delegates at the conference in Manchester, northern Britain.
It is expected that he will leave his post, which he has held since 1997, when Blair stands down in the course of next year.
Prescott, 68, appealed to the party to carry out an "orderly and peaceful" transition of power from Blair to his successor.
"We have learned the painful lessons of disunity in the past," he said.
Blair, who was forced by party rebels in early September to announce that he would leave as prime minister "within the next 12 months", was given a rousing and emotional farewell by delegates Tuesday.
However, the party conference ended with the race for his succession still wide open, and the prospect of a bitter leadership battle ahead.
Gordon Brown, the chancellor of the exchequer and "crown prince," failed to inspire the conference sufficiently to be Blair's undisputed successor, analysts said.
Earlier Thursday, Home Secretary John Reid delivered a tough message to Muslim extremists, saying Britain would not be "brow-beaten by bullies".
Reid, who was last week heckled by Muslim protesters during an address in east London, said a "life free from fear of terror and crime is the most basic of human rights".
There would be no "no-go areas" in Britain in the fight to tackle Muslim extremism, Reid told the conference.
During the protest against him last week, a well-known Muslim radical said to Reid: "How do you dare to come to our community?"
Reid, who is widely believed to be planning to put himself forward as a possible candidate to succeed Blair when he steps down, said there could be "no compromise with terrorism".
"When the terrorists or their loud-mouth advocates of terrorism sympathisers tell me that we won't be allowed to raise our arguments in this or that part of the community, my answer is simple: Yes, we will.
"This is Britain. There are, and will be, no 'no-go areas' in our country for any of our people, whatever their background, colour or creed. That's what it means to be British," Reid said.