A brace from Lukas Podolski gave Bayern the momentum after Ricardo Gardner had opened the scoring in the eighth minute with his first goal in almost five years.
But in Megson's fourth game in charge they showed a never-say-die attitude to stun the 66,000 capacity crowd at the Allianz Arena to secure a 2-2 draw.
Megson said: "We kept going. The attitude and application of the players was exceptional. When you come to a place like this teams can be beaten before they start.
"But we began brightly and got that goal from Ricardo, which was just what we wanted. It was a big night for us. The talent and quality of this Bayern team was there for all to see.
"Slowly but surely they came into the came into the game and (Franck) Ribery is as good a player as I have ever seen. He is a fantastic talent.
"We were without 12 players so those who came in deserve every credit.
"We had one or two were playing out of position but we will take a lot of confidence from this result."
Davies rocked the home crowd with his goal which came after Kevin Nolan showed his skills in the penalty area.
Megson added: "It was a great finish but you have to give Nolan credit for the work he put in to make the chance happen.
"He has been magnificent for me from day one and is a top class professional."
Megson said: "It was very encouraging - but then I've been hugely encouraged since day one, with the application.
"You've seen it tonight - they've stuck at it. We got away with it once or twice, but it was good.
"We keep drawing games. We had 12 players missing tonight against a club of this stature, and it was terrific."