The Italians dominated but Dickson Etuhu's away goal gives the Cottagers hope of overturning the deficit.
"It's not impossible. We're not out of it for sure," said Hodgson.
"I've seen stranger things happen in my career, so I am sure the players will be doing their very best to turn the game around in the second leg."
Fulham were behind in the Stadio Olimpico di Torino as early as the ninth minute, when Nicola Legrottaglie headed home from a corner.
A superb long-range drive from Jonathan Zebina midway through the first half and David Trezeguet's strike just before half time - in between which Etuhu struck for the visitors - gives Alberto Zaccheroni's side a healthy lead to carry into next Thursday's second leg at Craven Cottage.
Fulham have won plaudits this season for their performances in the Europa League, which has seen them claim impressive results against Basle and Roma and knock out holders Shakhtar Donetsk in the last 32.
Barring a spell in the first half, during which Etuhu claimed his goal, the Cottagers were second best against a strong Juve side.
"We showed for large parts of the game we were more than capable of matching them, but they have quality," former Inter Milan and Udinese boss Hodgson said."We had more situations around their goal than they had but they scored three and that's due to the quality players that they have. When the chances arose they took them."
However, Fulham are unbeaten at home in Europe this season, having won five out of six matches and Hodgson is predicting a compelling tie at Craven Cottage next week.
"There's no doubt we weren't favourites before tonight's game and we are even less favourites at 1-3 for the second leg but it will be an exciting game for us and for our public," he stated.
Source: BBC Sport
Source: BBC Sport