Dods, 37, started his career at Easter Road and is well aware of the Leith club's remarkable but unwanted record in the national cup competition.
It is 111 years since the trophy was paraded in Leith but Dods believes that will make Pat Fenlon's side all the more determined, especially given their crushing 5-1 defeat to Edinburgh rivals Hearts in last year's final.
He said: "When they were having good spells under Tony Mowbray and Alex McLeish, I thought that would be the time to break (the hoodoo).
"Last year they were struggling in the league but had a good cup run and you thought, with Hearts in the final, it was all set up for them to do it but they failed.
"But you think they can't keep going like that, that it's only a matter of time before they win it although I'm hoping it is not this year.
"I think they will be more determined than under pressure. Their form has shaded a wee bit lately but last season their form had shaded but they kept pulling it out in the cup and got to the final.
"They have had some tough ties on the way, beating Hearts in the first round, Aberdeen, then obviously winning away to Kilmarnock.
"So it is going to be hard for us but if we can go there and not be too nervous, get the ball down and pass then hopefully we can cause them problems.
"Who knows, they might have an off day and we can come up trumps."