Trailing 2-0 at Manchester City with only 20 minutes to go, it is little wonder Hodgson was feeling so pessimistic.
But, from nowhere, Fulham hauled themselves level before substitute Diomansy Kamara smashed home an injury-time winner which sets up a relegation showdown with Birmingham next week.
"The task looked very difficult, if not impossible," said Hodgson.
"I always felt if we could get one goal the tie was not dead but had the game gone longer, City might just have protected their lead.
"I am told we were relegated at one point, although I did not know it at the time, but now we have given ourselves a big chance."
With Birmingham leading Liverpool and Bolton ahead at Tottenham, Fulham were indeed down. However, now they are very much in the thick of the fight again, even if Hodgson accepts the task is not exactly an easy one.
"I challenged the players not to lose the second half but they went far beyond that, even if I would have found it difficult to envisage," said the Cottagers chief.
"We have brought ourselves into some kind of contention when most people had written us off. It is not going to be easy but at least we have some hope."