Danny Murphy scored the only goal of the game just before the hour mark to send Fulham to the top of Group E and leave them well-placed to reach the next round.
Fulham, who were missing a number of key players, rode their luck at times with Mark Schwarzer making a number of key saves and Hodgson was happy with his side's stubborn resistance as they held out for the three points.
"We were playing a good team, it was a very tough game.
"We were better in the second half, got on top and luckily scored our goal - but they made it tough in the final minutes.
"It was a gritty performance in terms of our defending - which is an important part of the game.
"We were able to rest one or two senior players, who I hope will recover for the weekend. It's important to use your squad in this competition."