NEW YORK, Nov 6 - The euro fell below $1.14 against the dollar on Thursday for the first time since late September, undermined by strong U.S. economic data that affirmed expectations of robust growth in the United States. The single European currency fell to a session low of $1.1398 after the release of the U.S. data, before rising to $1.1426 against the dollar, still down 0.06 percent on the day. Initial claims for state unemployment fell to 348,000 in the week ending Nov 1 from a revised 391,000 in the prior week. It was the lowest claims level since late January 2001. The consensus forecast was for claims of 380,000. U.S. non-farm business productivity, meanwhile, climbed at an annual rate of 8.1 percent in the third quarter.||