The Premier League 2 Division Two clash looked to be heading towards a stalemate at Whitley Park before Dylan Stephenson's drilled effort in the closing stages sealed maximum points for the young Magpies before City were reduced to ten men in stoppage-time following Jordan James' red card for dissent.
Muñoz, who joined the Magpies on an 18-month loan from Mexican top-flight side Santos Laguna in August, was delighted for Newcastle's youngsters to come out on top against their Blues counterparts.
"We're very happy with the win tonight," the 19-year-old striker told nufc.co.uk. "Everyone in the changing room is very pleased. We put in a lot of effort today and we were able to score in the last minute. We enjoyed the game and we enjoyed this win.
"It's a great feeling for the team to score right at the end! We worked a lot during the game on making sure we pressed and tried to get the ball into the box.
"With the goal, it's something that we really enjoyed. We had to be patient as we were playing against a good team.
"It's a very important win. We're now in third place and we are looking towards getting into the play-off spots. We'll be looking to keep up our form and need to be playing well and be together as a team."
After overcoming a long-term injury, Muñoz - who played 61 minutes against Birmingham - admitted he is determined to regain full fitness as well as learning to adapt to playing in a different country.
The North American youngster may be learning to grasp a new language but revealed he has been heavily supported by the Newcastle fans during his loan stint on Tyneside.
"I know the fans like that I'm here," the Mexican teenager, born in the United States, added. "When I arrived, I received a lot of positive messages and I really liked all the support they gave me. I really like the city, the Toon, I like it a lot! I want to thank the fans for their support!
"I'm very happy to be having minutes. I had an injury but I recovered and I'm working towards getting fully fit.
"It's very different from the football I'm used to playing in Mexico. I am getting used to the pace and physicality in England and I really enjoy every training session. I've been working hard and my team-mates and staff have been helping me too."