The young Magpies face the Millers, who were relegated from the Championship last term, at the New York Stadium (kick-off 7pm BST) and, after defeating Bradford City via penalties in their opening group fixture, can move into top spot of Group H with a victory after 90 minutes.
Diarmuid O'Carroll's side will be in confident mood, too, after recording a third consecutive win across all competitions last weekend, coming from behind to claim a 3-2 win against Aston Villa Under-21s in the Premier League 2.
Parkinson, who netted a brace against the Villans on Saturday, told newcastleunited.com: "The victory against Villa was a big one, especially coming from behind to win so everyone was buzzing with the performance and result. We are taking a positive attitude into the next match and it will be a challenge but I think the lads are ready for it.
"Bradford was our first win in the competition for a few years and going into this game against a League One side who will be pushing for promotion and played in the Championship last season, will be a test but we're all up for it.
"Since Diarmuid has come in, something he has tried to instill in us is that we're never down, never out, and always willing to fight until the end. I think we may have struggled with that last season, closing out games and picking up points when it mattered, but I think there's something about the lads this year which is really exciting and managing to win our last three games has been really good."
Parkinson will be aiming to continue his bright goalscoring form of late, with the Durham-born teenager targeting a sixth goal in as many away matches.
The 19-year-old, who made his Premier League debut for his boyhood club against AFC Bournemouth in November 2023, expressed his delight with his purple patch on the road as well as revealing a target he aims to reach before the turn of 2025.
He added: "I set myself a goal of trying to score 10 before January and I'm halfway there so far. I've been really pleased with how I've played and also how well I've done in front of goal so long may it continue.
"I quite enjoy playing away from home and the challenge of being in a different environment but I wouldn't say there's anything behind the current run. I've had a good couple of chances away from home and maybe not so many at home. Hopefully, I can get on the scoresheet again."
Matchday information for Newcastle United Under-21s' EFL Trophy to Rotherham United can be found here.
