Diomansy Kamara struck in the 66th minute to secure a creditable share of the spoils after Michel gave CSKA the lead at the Vasil Levski National Stadium.
Only John Pantsil and Simon Davies of the side that played against the Bulgarian league leaders can claim to be first-team regulars, a team selection that earned Hodgson some criticism.
But the Fulham manager felt his severely depleted line-up, which showed nine changes to the side that defeated Everton 2-1 on Sunday, justified his faith.
“The decision to pick the team we did was made with very careful thought and was backed up by the powers that be within the club,” he said.
“We made our mind up early on that if we are to do anything in this competition we’ll have to use as many players as UEFA allow us to.
“I think that now I can continue with this policy in the future.
“The team showed they deserved to be selected because we played against a good CSKA side.
“These players had a serious chance to show what they can do and proved why I can trust them.’’
Hodgson suspected a penalty should have been awarded to striker Erik Nevland shortly after CSKA scored the opener, an incident that happened in front of one of the new additional assistant referees.
“Erik is quite an honest player so for him to protest so vehemently that he was tripped up leads me to believe that he was,” he said.
“I didn’t notice the additional officials but I thought the referee and linesmen had good games because it was a fast match.”
CSKA SOFIA: Karadzhov, Kostadin Stoyanov, Minev, Kotev, Ivanov, Todorov, Yanev (Vladimir Manchev 78), Morozs (Marquinhos 46), Yanchev, Ivan Stoyanov (Michel 54), Delev.
FULHAM: Stockdale, Kelly, Pantsil, Baird, Smalling, Gera, Riise, Greening, Davies, Kamara, Nevland. Subs Not Used: Zuberbuhler, Watts, Saunders, Anderson, Uwezu, Marsh-Brown, Smith.
Referee: Darko Ceferin (Slovenia).