Ten-man Fulham looked to be heading for a famous win courtesy of Brede Hangeland's goal until Mario Andreolli popped up with the final kick of the game to earn Roma a point.
Stephen Kelly was sent off for Fulham in farcical circumstances as referee Paul Allaerts initially sent off the wrong player, brandishing the red card at Hangeland before finally dismissing Kelly.
Jeremy Menez saw his penalty superbly saved by Fulham keeper Mark Schwarzer and Hodgson was unhappy with the award of the penalty.
Hodgson was also amazed that the officials managed to get confused over the identity of which player to send off, even though the Europa League is using six officials in the competition.
"I've got my grave doubts as to whether it was a penalty, but they get given in those situations when a player drives into the box," said Hodgson.
Wrong player"They [the extra officials] got the wrong player with the red card but they should be making it clear that you can't give that as a last-man foul when someone [Hangeland] is coming across to cover.
"They brought their best players on, and we were short of numbers and we were short for a corner - which led to them equalising with the very last kick of the game.
"We had a marvellous first half - I thought we played very well. At half-time, we made some changes. But they bought on Mirko Vucinic and David Pizarro, two of their better players.
"It's very difficult to play with ten men. But I thought the effort was magnificent, and it was cruel.
"After conceding a 92nd minute goal with ten men against West Ham, this is very hard to take."