That game saw the Dons inflict a first Scottish Premiership defeat of the season on the Highlanders when Scott Vernon netted an undeserved winner.
Inverness now host Derek McInnes' men on Saturday and Irishman Doran admits his side are desperate to settle old scores.
He told CaleyJagsTV: "That game at Pittodrie hurt us. We didn't think we deserved to lose. They got one half chance and they took it.
"At the end of the game they celebrated like they had won the league. That shows how well we were doing at that stage in the season. We were unbeaten and they knew how big a scalp we were that day.
"Now we want to go out on Saturday and get our own back on them."
Caley Thistle overcame both Hearts and heavy winds to collect three points last weekend as Mother Nature blew down a storm on Tynecastle.
The wind and rain are forecasted to return on Saturday just as Inverness are kicking off at the Caledonian Stadium but Doran is not worried about his side's hopes being washed away by the wild weather.
"We are used to that kind of weather," said the 22-year-old. "We train at Fort George every day so we know what were are going to get when the wind gets up.
"Last Saturday, it worked for us because I think our players are more used to the conditions than the Hearts players were.
"It is supposed to be more of the same this weekend and that's good for our centre-halves. They like to get in and slide about and try to stop the opposition from scoring.
"We will relish the chance to play again in these conditions."
Billy McKay grabbed a double against the Jambos last week but it was midfielder Marley Watkins who stole the show with his crisp display and Doran believes there is more to come from the Englishman.
He said: "Marley is strong, powerful and quick and now he is finally getting his chance.
"He got injured in pre-season and it has taken him a while to get going again. But he is now showing what he can do."
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