Despite a positive opening from the young Magpies, Mark Cullen's poked finish gave Vale the lead five minutes before the half time break before Anderson, who signed his first professional contract at United last week, levelled the clash with a header courtesy of Jamie Sterry's delightful cross.
However, despite United's efforts for a late winner, Cullen netted his, and Port Vale's, second goal of the game after racing onto a through ball before rounding goalkeeper Jake Turner and placing the ball into an empty net to condemn Newcastle to a third defeat in Northern Group D, ending their campaign in negative fashion.
"The lads played well and we came out from the start and put a good shift in," Anderson told nufc.co.uk. "We played them off the park in the early stages and then came out in the second half and scored a very good goal which gave us a lot of confidence.
"It was annoying to concede the first goal just before half time as I thought we played well. We didn't expect it but credit to the team for bouncing back to get the equaliser after the restart.
"We were then unlucky to concede in the last minutes and we're gutted to lose. I thought we were the better team and deserved a lot more from the game."
Anderson, who lives in Whitley Bay but has represented Scotland at under-18 level, revealed his delight in scoring his maiden goal for the under-21 side - a week after turning 17 and signing a first professional deal with his boyhood club.
After playing in United's Northern Group D games against Macclesfield Town and Shrewsbury Town this term, Anderson believes he has learnt a great deal from featuring against Football League opposition and is determined to gain more opportunities for Newcastle's second-string.
"I was buzzing to score!" Anderson added. "At first, I thought I might have been offside and I was checking for the linesman but I was really happy to get my first goal. It was a good ball into the box by Jamie (Sterry) and I've managed to get onto the end of it.
"It's been a good couple of weeks for me after signing my professional contract but I know I need to keep working hard to get more opportunities like this. I just want to stay around the under-23 squad and try to get more minutes.
"I can take a lot of experience from playing in this competition. You have to be very switched on when you're out of possession to be in the correct positions for winning it back and trying to keep the ball because it can be hard to win it back."
