The right back put the ball into the net from a Lewis Vaughan cross just on half time, only for the linesman to raise his flag for offside.
However, replays show it was a shocker of a decision, with Tumilty clearly onside when the ball was crossed.
The goal would have seen Raith back on level terms with the Blues and Tumilty says he knew it was an incorrect call straight away.
“I can't remember the goal but I've been told there were a few passes in the build up and I've put it in.
“Even during the game I knew I was onside. I've since seen it on the BBC. It's really, really annoying.
“I was more than a yard onside, maybe two or three. I wouldn't like to be a lino but it's clearly onside.
"We felt quite comfortable and towards the end of the first half we were playing our best.
“We'd just come on to a game and were probably playing the better football so to get to 1-1 Dundee could get a bit nervous.
“There's so much riding on it for them so the goal could have made a big difference.”
The 24-year-old says he thought there was little between the sides in the 3-0 loss, but one man turned the game in Dundee’s favour.
"There wasn't much in the game,” he says, “then Charlie Adam s put a ball into the perfect position [for the first goal] like he's been doing all season.
“He was the difference. His passes are quality and if you give him time on the ball he's going to pick them out so we need to get a lot tighter on him in the next game.
"I felt at the start of the second half we were playing well but again Adam's put the ball where it's almost impossible to put it [for the second goal].
"You have to hold your hands up.”
It’s a seemingly impossible task for Rovers to get back into the tie at Dens Park on Saturday but Tumilty says they won’t go down without a fight.
"The next game we will have to go for pride, try not to lose it and see what happens.
“We won't go out with a whimper.”