The young Magpies lost 6-2 to a strong Saints team - which included the likes of England international James Ward-Prowse, Denmark international Pierre-Emile Højbjerg, Polish international Jan Bednarek and England under-21 internationals Sam McQueen, Alex McCarthy, Jack Stephens and Matt Targett - at St. Mary's on Monday night.
But three of the goals came in the final six minutes and 18-year-old full-back Kitchen told nufc.co.uk: "I thought we were going to get back into the game when it went to 3-2.
"We were a bit unlucky for the last 15 minutes with some of the goals that went in, so we're looking forward to the game on Friday and hopefully we'll get a good result.
"We've been speaking this week about how to press the ball with more intensity. The shape of the team was decent but if we can press with more intensity, hopefully we can get a few goals and win the game."
United haven't won a Premier League 2 game since August and have dropped to seventh in the table. Rovers, meanwhile, are third, four points behind leaders Middlesbrough.
Friday's game kicks off at 7pm UK time at Whitley Park in Benton. Admission is free to season ticket holders and members, otherwise it's £3 for adults and £1 concessions.
Kitchen, who turns 19 later this month, first trained with Newcastle's Academy at the age of six and was a regular for Dave Watson's under-18s last season.
He made his under-23s debut in a 0-0 draw at Brighton last month and also came from the bench against Southampton on Monday. He will be part of Peter Beardsley and Ben Dawson's squad for Friday's game.
"Physically, obviously it's harder but I think I've done quite well when I've come in," he said. "But the game's a lot quicker compared to under-18s.
"I try to keep everything quite simple, try to get the basics right, and then I like to get forward and get crosses in the box when I can."
Football runs in the family; his father, Sam, was a professional while his older brother Alex faced the likes of Romelu Lukaku as youngster with Newcastle, but didn't make the breakthrough to the first team.
"My dad played for Leyton Orient," explained boyhood United fan Ben. "My brother was a bit stronger physically, a bit bigger than me, but - and he won't like me saying this - I think I'm a bit better on the ball than he was.
"But if I was as good as my brother defensive-wise then I'd be happy, because he's a good defender.
"I want to play as many games as I can this season and try to impress, and try to make sure I stay here for as long as I can by getting another contract at the end of this year."
