Diego Forlan's 116th-minute strike ended the Craven Cottage side's hopes of ending an incredible 63-match campaign with a trophy, after Simon Davies had earlier cancelled out the Uruguyan international's first half opener.
Hodgson has transformed the fortunes of the modest West London outfit since his arrival in December 2007.
After saving the club from relegation on the final day of the 2007/08 Premier League season, the 62-year-old led them to seventh place last season and a mid-table finish this term, which has included an exhausting European tour that has stretched more than 20,000 miles.
Although the former Inter Milan and Blackburn Rovers boss has, arguably, taken Fulham as far as he or anyone else could ever have imagined, he stated after his side's defeat in Hamburg that he had no immediate plans to move on.
"I've been fully committed to Fulham as long as I've been here and always will be," he said.
"I still have a contract at Fulham and as far as I know that's where I'll be."
NEWS:Forlan double defeats Fulham
NEWS:Hodgson laments late strike
