The young Magpies broke the deadlock inside eight minutes of their Group H tie following a trialist's composed finish before Anderson, who made his Premier League debut against Arsenal in January, doubled the hosts' lead at Whitley Park after starting and completing a swift counter-attack.
Substitute Dylan Stephenson netted United's third in the closing stages, the striker's eighth goal of the season at second-string level, before Anderson added further gloss to the scoreline after scoring a stoppage-time penalty, registering a fourth goal in his last five competitive matches.
"It was a good performance," the 18-year-old told nufc.co.uk. "We've been working in training all week on how to beat Birmingham and I think we pulled it off perfectly. We kept a clean sheet as well, which is what we were looking for, and we played well.
"Getting the early goal lifted the confidence in the team and gives you that breathing space like it did against Middlesbrough a couple of weeks ago (a 4-1 win at St. James' Park). It gave us all a big boost and built momentum for us.
"It was good to score again. I actually dropped into a deeper role, ending up doing more stuff higher up the pitch. It gave me that opportunity to drive with the ball rather than having my back to play. It's good to get two goals and I need to keep working on my performances.
"The win puts us in good stead for the group. We need to make sure we come out of the next game with three points (against Huddersfield Town) too."
After an unforgettable few days for Magpies supporters since an investment group led by the Public Investment Fund (PIF) and also comprising of PCP Partners and RB Sports & Media, acquired the club on Thursday, Anderson admitted the news has been a ray of positivity for the squad.
"It's massive," Newcastle's second-string skipper added. "I think everyone has that energy in them that may have been missing before. It's exciting, everyone is buzzing around the place and are looking forward to see what is ahead.
"We're now the richest club in the world. It's crazy. For your hometown team to be that is really exciting."
