City meet the Jets at AAMI Park next Wednesday in the Cup's Round of 16.
The last time the two clubs met was in the A-League finals four months ago when Newcastle downed City 3-2 at McDonald Jones Stadium to book their place in the grand final.
Jamieson said the feeling of disappointment from that knockout match is still there among the City squad.
"Whenever you get knocked out in a final series I don't think that feeling necessarily goes," he told FourFourTwo.
"It's a case of accepting it but always having that disappointment lingering because you don't want to feel it again.
"In regards to that game, we were up 1-0 and then the circumstances of both goals, one being quite a freakish goal and one being a goal that maybe we could have done a bit better with. It still hurts a bit.
"But for us, we've accepted it, we look upon the new season as a new start and one that we definitely feel we want to do really with. The Newcastle Jets game might have a little bit more to it from the media's perception because of the game last year and that we were knocked out of the semi-final.
"Regardless of who we're playing we want to win, but it's always good to try and play a team that knocked you out of the finals and do them over."
City earned their place in the last 16 by beating Brisbane Roar 1-0, while the Jets defeated Gold Coast Knights 1-0.
Fullback Jamieson is expecting another tough encounter with Newcastle.
"It's not going to be an easy game," the 29-year-old said.
"They're obviously a team that surpassed all expectations last year in their league position and they've kept a very similiar squad I would say.
"We take any A-League opposition with a massive amount of respect but having the impetus of having another competitive game if we do win gives us the motivation to do well."