The Cottagers took an undefeated record of one win and two draws into the clash at Rome's Stadio Olimpico and went 1-0 up in the first half before disaster struck and they had two players sent off as the home side came from behind to grab all three points.
The loss leaves Fulham in third place in their group with five points, behind Roma and FC Basel, and with a home game against CSKA Sofia and a clash with Basel remaining, their chances of qualifying for the next phase still hangs in the balance.
"Every time you get players sent off you have players suspended for three matches which means, at this rate, I would need to have a squad of 60 players.
"Unfortunately, this defeat takes things out of our hands a little bit. We could win the last two games and still not qualify.
"It has been an interesting experience," Hodgson added. "We will become stronger and bounce back."