Brian McBride and Erik Nevland scored in each half to register the Cottagers' first away win in the league since September 2006, a sequence spanning 33 games.
The result has left Fulham four points adrift of safety with four games remaining and Hodgson refused to rule out an unlikely escape act.
"Whichever two teams go down now, it will be major disappointment," he said. "We've made it hard for ourselves but we're still in the race and while you're in the race there's always the chance you'll find the sprint that will take you past your rivals.
"I was told last week, after we had been beaten 3-1 by Sunderland, that we had no chance. We'll get good reports and judgment on our play today, but we've had other games where we haven't played too badly but lost narrowly. This was a good performance defensively and I also thought we attacked well.
"I'm having to be careful about what I say given it was reported after the Sunderland game that I was crying. I'm very satisfied with the team's performance but disappointed we still have it all to do.
"We have this huge mountain to climb and deficit of points to make up but I'm encouraged after last week, which was very disappointing."
Hodgson hailed McBride's performance and declared the USA striker has a key role to play in Fulham's battle against relegation.
"It's not been easy for Brian coming into the team after suffering that knee injury when so much is expected of him, but he got better as the game went on," Hodgson said.
"He gives us shape and linked well with David Healy. His work rate is crucial for us."
Boss Steve Coppell admitted the result has ensured the Royals' own battle against relegation will go down to the wire.
"We were poor today and there are no excuses. They were better than us, deserved to win and the result was no accident," he said.
"We won't come up with any defence. We will take it on the chin and have a go next week.
"Winning today would have put us in a really strong position. Instead, losing puts us in a difficult situation and it's all for us to do now."