Before then, Fulham face Sunderland at Craven Cottage on Sunday then travel to Burnley before playing in Switzerland.
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Hodgson said: "The Premier League is the major concern and the Europa League comes second to that.
"I don't think the fans will hold anything against us for our performances in this competition. They know when we go to Basle we will be doing our very best.
"We are still trying to do the best we can, the players will be trying hard to get us through and that was evident against CSKA, personified by people like Simon Davies, Zoltan Gera and Bobby Zamora.'
Basle lost 2-1 in Rome so they also need something from the game against Fulham, with a point enough to take them into the knockout stages.
"We knew it would be tough for Basle to get anything at Roma so with the four points dropped against Roma we always thought we would have had to win the last two games."
Before Gera's 15th-minute winner, Danny Murphy missed a penalty on his return to action after six weeks out with a knee injury.
"He's our penalty taker," Hodgson said. "It was the first missed since I've been at the club. It wasn't a mistake to let him take it.
"It was foolish to miss a penalty but there were other missed chances and the game could have been dead and buried.
"I'm very pleased that we showed the strength of character to stand up to that."
Hodgson was without six players through injury and suspension and will today assess a possible calf injury Simon Davies suffered in the second half.