Tom Watson said he had been thinking about quitting as Labour election co-ordinator "for a few months", because he found the post very tiring and felt unable to speak out on issues of concern.
He told BBC Radio WM: "We have had all this fuss over Falkirk and I just thought to myself, if I am getting into the story and not being useful any more for Ed, then it's time to move.
Asked about the details of what had happened in Falkirk, he said: "I really don't know about that. One of the things I did on Falkirk was keep out of that process, because there's an employee of mine who was a candidate.
"I know this works - people put two and two together and very often get five, but that's not the reason I have gone. The Falkirk thing crystallised in my mind how difficult it would be for me to stay in the post."
He added: "I've had an unusual journey in politics. There are some people who have never quite forgiven me for resigning in 2006 under Tony Blair and I accept that completely. What I don't want to be is a problem for Ed Miliband, so going to the backbenches is the best thing.
"I want him as Prime Minister and he has got my full support."
Tom Watson, who resigned from the shadow cabinet yesterday over the Falkirk selection controversy, said the Conservative party's portrayal of trade union Unite being in control of Labour was "just not true".
Speaking to BBC Radio WM, Mr Watson said: "Looking at how the unions organise within the Labour Party, I genuinely think they are pretty hopeless. I don't think there's many trade union activists who get much of a say these days. I don't think it's a problem.
"I do think there's a lot of politics behind it. Obviously David Cameron would like people to believe that the Labour Party is in the hands of these left-wing factions. It's just not true.
"We've got to sort these arrangements out - clearly something had gone wrong in Falkirk that needs sorting out - but I think David Cameron's portrayal of the situation, that everyone is in hock to Len McCluskey, is just not true."
Tom Watson has posted his resignation letter to Labour leader Ed Miliband on his blog. A extract of it reads:
Tom Watson, the Labour MP for West Bromwich East, has resigned from his shadow cabinet role as general election co-ordinator, he has said on his blog.
Deputy Chair of the Labour Party and MP for West Bromwich East Tom Watson will give evidence at the Leveson Inquiry later today.
West Bromwich East MP Tom Watson is due to give evidence at the Leveson Inquiry next week.
Labour MP for West Bromwich Tom Watson, a member of the culture, media and sport select committee which had previously questioned Rupert and James Murdoch, says he is unconvinced by Rupert Murdoch's appearance at the Leveson Inquiry.