The League One club caused a major shock in the fourth round of the FA Cup by seeing off Premier League leaders Chelsea 4-2 at Stamford Bridge.
And having made the League Cup final in 2013 - a run that included wins over Arsenal and Aston Villa - Parkinson says positivity will be the order of the day at Valley Parade this weekend.
"We're up against a good side but our aim is to put in a really good performance like we've done so far in this competition and we'll see where it takes us," Parkinson explained on Friday.
"No-one expected us to be here when we drew Chelsea so it's a bonus game for us but of course we want to give a good account of ourselves.
"We're going to have to play right at the top of our game, Sunderland are going to have to have an off day and we're going to have to play like the underdogs, which is do everything we can do but better than we've done before.
"We always talk about performance levels but we know were up against a good side. I saw [Sunderland] play against Fulham and they were outstanding.
"But we're going to attack and be positive, that's the way we play, we won't be sitting back on the day, we'll be looking to get forward at every opportunity.
"Like I said after the Chelsea game, we're at our best when were in a positive state of mind."
Parkinson has no fresh injury concerns ahead of the tie, while his opposite number Gus Poyet could welcome back Jack Rodwell and Billy Jones to the fold after their respective groin and hamstring injuries.
The Uruguayan will, however, be without Lee Cattermole (knee), Will Buckley (knee), Anthony Reveillere (hamstring) and Emanuele Giaccherini (illness).
As Poyet prepares to avoid becoming the latest casualty to fall at the hands of Bradford, winger Adam Johnson is under no illusions as to what 2014 League Cup finalists Sunderland need to do to if they are to play at Wembley for a second season running.
"They beat Chelsea in the last round and that can happen to anyone so we need to go there and put Tuesday’s result behind us, and go on the front foot straight away to put them under pressure," Johnson told the club's official website after their midweek defeat to QPR.
"If we get past Bradford and we get another favourable draw we could go to Wembley for a semi-final which is great, but I think our main aim is obviously the league which everyone knows."
