Fortune produced "an encouraging performance" and welcomed included newcomers David Brown and Paul Stein, went unrewarded as Redbridge's two first half goals – one a hotly-disputed goal very early in the game – gave them the points.
Substitute Elliott Mayer's second-half goal reduced the deficit but Fortune could not force an equaliser.
TFFC's Connor Brand and an opponent were sent off for violent conduct and Fortune were left enduring another defeat.
Fortune boss Simon Linden told JC Sport: "After a few weeks off, it was good to return to action and we were unlucky to not get something out of the game.
"It’s been an extremely tough season, with lots not going our way but credit where it’s due, the lads worked hard today and David Brown's volley just wide in injury time may have won us a point.
"It will be good to get away from league action next week and play in the cup."