The veteran made the announcement following the Trotters 1-0 win against Crystal Palace yesterday ending weeks of speculation over the future of the former Newcastle man.
Speed feels that he will not be able to combine his club commitments and any potential management role but has warned that the FAW must take their time in appointing a successor to Mark Hughes.
"If you've got aspirations to be a manager or coach, obviously coaching your country would be a great honour," Speed told the BBC
"But you only get one shot at it really and for me this time I don't think I could give it my full attention.
"We want the best man for the job and I don't think that's me at the moment. I definitely won't be applying for it. There has been a lot of talk but what is most important is that we get the best man for the job, irrespective of who wants who and who wants somebody else.
"The most important thing has got to be Welsh football and whoever does get the job then everyone, players, fans, press, get behind him and hopefully Welsh football can progress