The young Magpies take on City's second-string at Whitley Park (kick-off 1pm GMT) but are unable to progress into the knockout stages of the competitions after losing their opening four group matches.
Despite the result having no effect on the final standings of the table, Crossley - who signed his first professional contract with the Magpies last summer - believes the contest can benefit the group ahead of an important run of fixtures in the Premier League 2.
The 18-year-old, who primarily plays on the left wing, told nufc.co.uk: "Although we are out of the Premier League Cup, we have been treating it like a league game and making sure we are training hard every day to improve and be as prepared as possible.
"We know Sunderland is our next league gam so to start well against them would be brilliant and we know that could come from a good team performance and a win against Bristol City."
Newcastle's second-string were victorious in their previous Premier League Cup encounter, a dramatic 3-2 victory away at Crystal Palace after recovering from a 2-1 deficit by scoring two goals deep into stoppage-time.
The Murton-born teenager, one of a handful of youngsters to feature on the bench during Newcastle's 2-1 friendly victory against La Liga outfit Rayo Vallecano in December 2022, is hoping United's youngsters can take inspiration from their spirited comeback against the Eagles heading into the cup clash against the Robins.
Crossley, who scored on his debut for Newcastle's under-21 side against Crystal Palace's second-string at the tender age of 16, added: "The game against Crystal Palace was a great battle from the team. We fought until the very end, having that heart and fight we had in the game to come away with the victory.
"We'll be hoping to bring it into tomorrow's game and it would be a great help for us to go on and win the match against Bristol City."
Spectators can attend Wednesday's Premier League Cup clash at Whitley Park, with season ticket holders gaining free admission, otherwise it's £3 for adults and £1 concessions.
